M.M. Quick Tutorial

Introduction

ModelMicrobiome is a novel platform for testing the performance and assumptions underlying ecological inference of microbiomes. Whereas previous benchmarking and modeling efforts have used case-control frameworks, and/or used randomized real data, none have tested the accuracy of ecological inference following a sequence count normalization procedure. Previous efforts have focused on the ability to accurately detect a change in relative abudance (i.e. differential abundance analysis). But these tests do not reflect how well the ecological relationships are preserved through the normalization process (e.g. relationship between the taxa and their environment or among taxa). This software does not attempt to address bias that is introduced by the sequencing, DNA purification, or field sampling efforts. It only is meant as a tool to better understand the effect that any post-hoc sequence count normalization has on our ability to infer underlying ecological relationships.

To further clarify the limits of this software, it is not intended to be applied to metagenomics analyses that derive from shotgun sequence data. There are database and sequencing biases that are particular to whole genome sequencing that must be addressed separately and that may confound the inferences made from this software. THIS SOFTWARE IS NOT DESIGNED TO ADDRESS SHOTGUN SEQUENCING OR ION TORRENT ETC. SEQUENCING. This software is designed specifically for amplicon (i.e. metabarcoding) studies of a single gene locus used to infer population structure. For more detailed information about how the indexes are constructed, refer to (DOI: … )

This software was written under R version 3.6.1. R version 4 has been published with major updates to some of the core mechanics. Model.MicrobiomeV2 will be updated for R 4.0 soon.

This tutorial will address the primary functionalities of Model.Microbiome, and provide an example of how it can be used in the course of an experimental workflow.

Install Model.Microbiome

First, let’s install Model.Microbiome:

# update anything from my local computer (for me as I work, not you...) ####
#setwd("/Users/maullabmacbookpro/Documents/GitHub/Model.Microbiome")
#library(devtools)
#library(roxygen2)
#document()

#now install ####
devtools::install_github("djeppschmidt/Model.Microbiome")

## Skipping install of 'Model.Microbiome' from a github remote, the SHA1 (775db361) has not changed since last install.
##   Use `force = TRUE` to force installation

Now load all the other packages we need (or download and load if you haven’t already):

# load required packages ####

library(Model.Microbiome)
library(reshape2)
library(ggplot2)
library(vegan)

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library(dplyr)

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library(plyr)

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library(phyloseq)
library(viridis)

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library(ranacapa)
library(edgeR)

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library(limma)
library(GLDEX)

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library(stats)
library(igraph)

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library(car)

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library(DESeq2)

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The core functionality of Model.Microbiome is to create a model microbial community, then simulate sequencing by subsampling from it. This simulated count data can then be normalized using any normalization method. This is handled by the run.analysis2() function. I recommend running this function with SuppressWarnings(). It is normal for the linear model functions that Model.Microbiome references to give warnings whenever the fit is perfect; these warnings stack up across the simulation and become overwhelming.

Building the model community works sequenially by: 1. creating an environment made out of 5 environmental parameters, 30 sites, and 6 statistically distinctive “experimental” conditions. a. environmetnal paramters 1-3 change in mean and variance according to the experimental condition. b. environmental parameters 4 and 5 are unrelated to the experimental design, but do affect taxon abundance c. the sampling environment consists of 30 samples, divided into 6 experimental conditions/treatment (or 5 reps per condition) d. the environmental parameters have the same mean and variance within each condition/treatment every time the software is run; however, the values of any given run are randomly drawn from this distribution. Therefore no two runs will have exactly the same environment, but they will represent exactly the same experiment.

2. Choosing which species exist in each sample.

1. The user sets how many taxa will be chosen per sample
2. the user sets how many taxa will be chosen per experimental treatments
3. the user sets how many taxa will be chosen to be globally distributed

NOTE: SEE SECTION DETAILS FOR CAVEATS ABOUT THIS SELECTION PROCESS!!

3. Community assembly.

1. taxon abundances are calculated; each species has a specific relationship with the environmental variables.
2. OTU table generated, and merged into a phyloseq object with metadata on the environment, etc.

NOTE: While Model.Microbiome does construct networks and taxon associations in downstream analyses, it does not model those relationships explicitly; no species function refers explicitly to another species.

4. Community is sampled

1. this is a subsampling routine that creates the “sequence output” table

5. Sequence Normalization

1. Model.Microbiome applies user-supplied normalization functions to the subsampled data table, and generates metrics to aid with interpretation. It can accommodate any number of arbitrary methods.

So let’s look at the function. It has several inputs necessary:

commonN: Number of taxa that have a global distribution groupN: Number of taxa that are group-specific singleN: Number of taxa that are sample-specific

NOTE: there are 700 species functions that the software selects from. For each of these values, it uses a random selection routine. It includes resampling among the groups. This means that:

THERE IS A CHANCE THAT A TAXON MAY END UP REPRESENTING SEVERAL GROUPS, OR SAMPLES.

D: mean sampling depth (i.e. simulating sequencing) V: variance of sampling depth.

method: names of the functions to be used for count normalization (see below for details)

Let’s look at an example using a narmalization method included with Model.Microbiome.This implementation creates a single output object that contains the phyloseq objects created before, and a number of different statistics. In order to get it to work, we need at least one methods function:

method<-c("QSeq")

model<-suppressWarnings(run.analysis2(commonN=30, groupN=20, singleN=5, D=500, V=250, method))

Note that rarefaction curves are generated automatically for the reference condition in each simulation run. This helps us judge whether our subsampling level is under sampling in general. It also allows us to examine the diversity of each samople; we can see that there are distinctions in diversity among the experimental conditions.

The QSeq method is a native Model.Microbiome method, but let’s look at how it was constructed to give a framework for how the user can create functions that work with Model.Microbiome:

# these functions are already provided as a part of Model.Microbiome
make.scaled2<-function(ps, val, scale){
  scaled<-data.frame(mapply(`*`, data.frame(as.matrix(otu_table(transform_sample_counts(ps, function(x) x/sum(x))))), scale * val))# sample_data(ps)$val))
  names<-rownames(data.frame(as.matrix(otu_table(ps))))
  rownames(scaled)<-names
  scaled<-round(scaled)

  p2<-ps
  otu_table(p2)<- otu_table(scaled, taxa_are_rows=T)
  p2
}

QSeq<-function(ps){
    scale<-sample_data(ps)$DensityF
    out<-make.scaled2(ps, val=2*mean(sample_sums(ps)), scale)
    out
}

Notice that this is actually one function nested within another. The wrapper helps the function to play nice. It’s easy to replicate wrappers to provide the underlying function with different inputs if we want to test the different potential conditions. For example, our QSeq function is meant to replicate the normalization technique called quantitative sequencing. This technique combines quantitative data from QPCR with sequence count distributions to normalize the sequence counts in each sample by the relative total sequence counts of that sample compared to other samples. This should more closely approximate the behavior of the sampled community than relative abundance. To do this though, we need to decide what the mean value for the sample-wise abundance normalization. We could make several versions of the QSeq function to test what is the optimal mean sample-wise total abundance. To do this we change the value parameter as follows:

QSeq0.5<-function(ps){
    scale<-sample_data(ps)$DensityF
    out<-make.scaled2(ps, val=0.5*mean(sample_sums(ps)), scale)
    out
}

QSeq1<-function(ps){
    scale<-sample_data(ps)$DensityF
    out<-make.scaled2(ps, val=mean(sample_sums(ps)), scale)
    out
}

QSeq2<-function(ps){
    scale<-sample_data(ps)$DensityF
    out<-make.scaled2(ps, val=2*mean(sample_sums(ps)), scale)
    out
}

QSeq3<-function(ps){
    scale<-sample_data(ps)$DensityF
    out<-make.scaled2(ps, val=3*mean(sample_sums(ps)), scale)
    out
}

QSeq10<-function(ps){
    scale<-sample_data(ps)$DensityF
    out<-make.scaled2(ps, val=10*mean(sample_sums(ps)), scale)
    out
}

QSeq100<-function(ps){
    scale<-sample_data(ps)$DensityF
    out<-make.scaled2(ps, val=100*mean(sample_sums(ps)), scale)
    out
}

In this way we end up with a number of different functions that can be called independently, but that work on the same underlying mechanic. This is important if we have a method that we want to optimize in some way.

If we want to use all of our methods in our simulation study, then we simply do:

method<-c("QSeq0.5", "QSeq1", "QSeq2", "QSeq3", "QSeq10", "QSeq100")

Then we implement it in the analysis pipeline:

model<-suppressWarnings(run.analysis2(commonN=30, groupN=20, singleN=5, D=500, V=250, method))

We can call the phyloseq object from any one of the normalization (including the reference data and the raw sequence counts):

model$model$comm
model$raw$comm
model$QSeq0.5$comm
model$QSeq1$comm
model$QSeq2$comm
model$QSeq3$comm
model$QSeq10$comm

Model.Microbiome also automatically calculates several metrics. For example, it calculates automatically an experiment-wide PERMANOVA for each method and each factor. So for example if we look at the reference, we have a seperate permanova for the experimental category:

model$model$PERMANOVA$Category

## 
## Call:
## adonis(formula = x ~ Factor2, data = y) 
## 
## Permutation: free
## Number of permutations: 999
## 
## Terms added sequentially (first to last)
## 
##           Df SumsOfSqs MeanSqs F.Model     R2 Pr(>F)    
## Factor2    5    5.7833 1.15665  47.094 0.9075  0.001 ***
## Residuals 24    0.5895 0.02456         0.0925           
## Total     29    6.3727                 1.0000           
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

And each of the environmental factors:

model$model$PERMANOVA$F1

## 
## Call:
## adonis(formula = x ~ F1, data = y) 
## 
## Permutation: free
## Number of permutations: 999
## 
## Terms added sequentially (first to last)
## 
##           Df SumsOfSqs MeanSqs F.Model      R2 Pr(>F)    
## F1         1    1.1235 1.12347  5.9927 0.17629  0.001 ***
## Residuals 28    5.2492 0.18747         0.82371           
## Total     29    6.3727                 1.00000           
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

model$model$PERMANOVA$F2

## 
## Call:
## adonis(formula = x ~ F2, data = y) 
## 
## Permutation: free
## Number of permutations: 999
## 
## Terms added sequentially (first to last)
## 
##           Df SumsOfSqs MeanSqs F.Model      R2 Pr(>F)   
## F2         1    0.8850 0.88502  4.5156 0.13888  0.003 **
## Residuals 28    5.4877 0.19599         0.86112          
## Total     29    6.3727                 1.00000          
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

model$model$PERMANOVA$F3

## 
## Call:
## adonis(formula = x ~ F3, data = y) 
## 
## Permutation: free
## Number of permutations: 999
## 
## Terms added sequentially (first to last)
## 
##           Df SumsOfSqs MeanSqs F.Model      R2 Pr(>F)    
## F3         1    1.7116 1.71160  10.282 0.26858  0.001 ***
## Residuals 28    4.6611 0.16647         0.73142           
## Total     29    6.3727                 1.00000           
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

model$model$PERMANOVA$F4

## 
## Call:
## adonis(formula = x ~ F4, data = y) 
## 
## Permutation: free
## Number of permutations: 999
## 
## Terms added sequentially (first to last)
## 
##           Df SumsOfSqs MeanSqs F.Model     R2 Pr(>F)  
## F4         1    0.4034 0.40338  1.8921 0.0633  0.076 .
## Residuals 28    5.9693 0.21319         0.9367         
## Total     29    6.3727                 1.0000         
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

model$model$PERMANOVA$F5

## 
## Call:
## adonis(formula = x ~ F5, data = y) 
## 
## Permutation: free
## Number of permutations: 999
## 
## Terms added sequentially (first to last)
## 
##           Df SumsOfSqs MeanSqs F.Model      R2 Pr(>F)  
## F5         1    0.4381 0.43805  2.0667 0.06874  0.063 .
## Residuals 28    5.9347 0.21195         0.93126         
## Total     29    6.3727                 1.00000         
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

We can compare any of these across treatments:

model$model$PERMANOVA$F1 # reference condition!

## 
## Call:
## adonis(formula = x ~ F1, data = y) 
## 
## Permutation: free
## Number of permutations: 999
## 
## Terms added sequentially (first to last)
## 
##           Df SumsOfSqs MeanSqs F.Model      R2 Pr(>F)    
## F1         1    1.1235 1.12347  5.9927 0.17629  0.001 ***
## Residuals 28    5.2492 0.18747         0.82371           
## Total     29    6.3727                 1.00000           
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

model$raw$PERMANOVA$F1 # not normalized

## 
## Call:
## adonis(formula = x ~ F1, data = y) 
## 
## Permutation: free
## Number of permutations: 999
## 
## Terms added sequentially (first to last)
## 
##           Df SumsOfSqs MeanSqs F.Model      R2 Pr(>F)    
## F1         1    1.0582 1.05818  4.2325 0.13131  0.001 ***
## Residuals 28    7.0003 0.25001         0.86869           
## Total     29    8.0585                 1.00000           
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

model$QSeq0.5$PERMANOVA$F1 # lowest mean value

## 
## Call:
## adonis(formula = x ~ F1, data = y) 
## 
## Permutation: free
## Number of permutations: 999
## 
## Terms added sequentially (first to last)
## 
##           Df SumsOfSqs MeanSqs F.Model      R2 Pr(>F)    
## F1         1    1.1141 1.11410  5.7043 0.16925  0.001 ***
## Residuals 28    5.4687 0.19531         0.83075           
## Total     29    6.5828                 1.00000           
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

model$QSeq1$PERMANOVA$F1  #...

## 
## Call:
## adonis(formula = x ~ F1, data = y) 
## 
## Permutation: free
## Number of permutations: 999
## 
## Terms added sequentially (first to last)
## 
##           Df SumsOfSqs MeanSqs F.Model      R2 Pr(>F)    
## F1         1    1.1125 1.11252  5.7102 0.16939  0.001 ***
## Residuals 28    5.4552 0.19483         0.83061           
## Total     29    6.5678                 1.00000           
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

model$QSeq2$PERMANOVA$F1 #...

## 
## Call:
## adonis(formula = x ~ F1, data = y) 
## 
## Permutation: free
## Number of permutations: 999
## 
## Terms added sequentially (first to last)
## 
##           Df SumsOfSqs MeanSqs F.Model      R2 Pr(>F)    
## F1         1    1.1122 1.11218   5.708 0.16934  0.001 ***
## Residuals 28    5.4557 0.19485         0.83066           
## Total     29    6.5678                 1.00000           
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

model$QSeq3$PERMANOVA$F1 #...

## 
## Call:
## adonis(formula = x ~ F1, data = y) 
## 
## Permutation: free
## Number of permutations: 999
## 
## Terms added sequentially (first to last)
## 
##           Df SumsOfSqs MeanSqs F.Model      R2 Pr(>F)    
## F1         1    1.1126 1.11256  5.7076 0.16933  0.001 ***
## Residuals 28    5.4580 0.19493         0.83067           
## Total     29    6.5705                 1.00000           
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

model$QSeq10$PERMANOVA$F1

## 
## Call:
## adonis(formula = x ~ F1, data = y) 
## 
## Permutation: free
## Number of permutations: 999
## 
## Terms added sequentially (first to last)
## 
##           Df SumsOfSqs MeanSqs F.Model      R2 Pr(>F)    
## F1         1    1.1120 1.11198  5.7058 0.16928  0.001 ***
## Residuals 28    5.4568 0.19489         0.83072           
## Total     29    6.5688                 1.00000           
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

model$QSeq100$PERMANOVA$F1# highest mean value

## 
## Call:
## adonis(formula = x ~ F1, data = y) 
## 
## Permutation: free
## Number of permutations: 999
## 
## Terms added sequentially (first to last)
## 
##           Df SumsOfSqs MeanSqs F.Model      R2 Pr(>F)    
## F1         1    1.1120 1.11202  5.7062 0.16929  0.001 ***
## Residuals 28    5.4567 0.19488         0.83071           
## Total     29    6.5687                 1.00000           
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

You’ll notice that the QSeq PERMANOVA tables are very similar to the reference PERMANOVA table, and that the un-normalized table is a bit different. This is great! It tells us that we are recapturing some lost information from the subsampling.

Model.Microbiome uses a few metrics to understand bias that is introduced through the normalization process. All the metrics in Model.Microbiome consist of the ouput from an analysis conducted on a normalized dataset (treatment) divided by the same analysis conducted on the reference community. For example, if we are interested in the relationship between a taxon an the environment, we could construct a linear model where abundance of taxon x depends on environment A. The R-squared of this model would represent the amount of information captured by the model. If we applied this model to both the reference community, and the normalized community, then we have a measure of the “actual” relationship and the inferred relationship after our normalization, respectively. The ratio of these values gives us a comparable value where 1 represents a perfect match; greater than 1 indicates the normalization method leads to overestimating the explanatory power of the environmental factors on the abundance of the taxon; and a value of less than one indicates that the normalization underestimates the explanatory value of the environmental parameter. All of the indices are based on this interpretation principle.

Here is a brief description of each index:

Loss of information index (LII) is based on a linear model approach, but instead of regressing the taxa against the environment and comparing the outputs, it regresses the treatment (normalized data) against the reference (pre-sampling). Thus the R-squared value of the model is a direct measure of how well reference abundance predicts the normalized abundance. The LII output has several components;

$Index : index value which is the sum from all taxa of (1 - the linear regression r-squared values) divided by the total number of taxa. This is a single value for the whole run. Lower scores equate to less overall information lost. The LII can be interrpeted as “mean information lost per taxon”

$R : a named list of the R squared values that are summed in the Index, one per taxon in the run.

$diff : a list of (1 - the r-squared values) for the Index value, one for each taxon. This is useful to identify which taxa are deviating substantially, and help with troubleshooting the normalization method, and identifying why any patterns might exist.

All of these can be accessed from the output object (see output object map).

The second set of metrics consist of linear regressions of the taxa (or whole community) against environmental and experimental design predictors. This test allows us to diagnose the effect that our normalization protocol has on our ability to infer relationships between the taxa and the environment / experimental condition. The primary outputs of this process are then taken as a ratio to the reference for interpretation.

$lmRatiotab : list of taxa and their R-squared values between taxon and the environment, normalized by the reference

$lmRatiotab.model : list of taxa and their R-squared values between taxon and the experimental design, normalized by the reference

lmRatiotab or lmRatiotabl.model values that are close to 1 represent near perfect retention of the ecological relationship. Values that approach 0 or are above 1.5 represent substantial loss of accuracy. There should be no negative values.

There are also metrics that reflect beta diversity. The R-Squared value for a PERMANOVA analysis of the experimental conditions, and environmental parameters against a Bray-Curtis transformed count table are used to calculate a R-Ration between the reference community and the treatment communities. Also, modularity is calculated based on a correlation matrix using a number of different construction methods. These methods will be addressed in more detail later.

#Object Map:

Output Object Map

The speciesMeta object stores a few taxon-specific metrics that help us interpret the outcomes;

$prevalence is a taxon-wise measure of how many sites the taxon actually occures in (in the reference community).

$mean_abundance is a taxon-wise measure of the mean abundance of each taxon across all sites (in the reference community)

$sd_abundance is a taxon-wise measure of the standard deviation in abundance of each taxon across all sites (again, reference community).

$M.Eval is the mean of the relative abundance of the taxon at each site divided by the sampling depth of that site. This is meant to represent an unweigthed estimation of the likelihood that a taxon will be sampled at any site, given that they exist in that site. Lower values mean the taxon is generally less abundant, and less likely to be sampled in any of the sites.

These taxon-specific data can be useful for exploring patterns when it’s time to interpret an experimental run. Let’s look at some example plots that demonstrate the utility of these metadata:

First, let’s examine the relationship between the expected likelihood of sampling a taxon and the amount of information that is lost. In this plot, the method (QSeq0.5) axis represents 1-(r-squared of treatment vs reference) abundance values for each taxon in the community. Thus higher values equate to more information lost:

ggplot(model$model$SpeciesMeta, aes(x=log10(M.Eval),y=log(QSeq0.5), col=prevalence))+
  geom_point()+ 
  scale_color_viridis_c(option="C")+
  theme_classic()

The color represents the prevalence, we can see that in this case, there are many taxa that lose no information (along the bottom of the graph). Most of these are taxa that only occur in one sample. Let’s color the samples differently:

ggplot(model$model$SpeciesMeta, aes(x=M.Eval,y=QSeq0.5, col=log(mean_abundance)))+
  geom_point()+ 
  scale_color_viridis_c(option="C")+
  theme_classic()

ggplot(model$model$SpeciesMeta, aes(x=log(M.Eval),y=log(QSeq0.5), col=log(mean_abundance)))+
  geom_point()+ 
  scale_color_viridis_c(option="C")+
  theme_classic()

We can see that taxa with high mean values are much more likely to retain their information through the sampling.

ggplot(model$model$SpeciesMeta, aes(x=log10(M.Eval),y=log(QSeq0.5), col=log(mean_abundance)))+
  geom_point()+ 
  scale_color_viridis_c(option="C")+
  theme_classic()

ggplot(model$model$SpeciesMeta, aes(x=log10(M.Eval),y=log(QSeq1), col=log(mean_abundance)))+
  geom_point()+ 
  scale_color_viridis_c(option="C")+
  theme_classic()

ggplot(model$model$SpeciesMeta, aes(x=log10(M.Eval),y=log(QSeq10), col=log(mean_abundance)))+
  geom_point()+ 
  scale_color_viridis_c(option="C")+
  theme_classic()

ggplot(model$model$SpeciesMeta, aes(x=log10(M.Eval),y=log(QSeq100), col=log(mean_abundance)))+
  geom_point()+ 
  scale_color_viridis_c(option="C")+
  theme_classic()

We can see that in particular there is a shift in the amount of information that is lost in the middle M.Eval ranges; at high E.Val, there is relatively less information lost and so the values are more stable. At the low end, the lost information effects are dominated by whether or not the taxa happen to be detected; in the middle, taxa are regularly detected but their abundance is very dependent on sampling depth of the sample. Thus this is the area where we regain the most information.

ggplot(model$model$SpeciesMeta, aes(x=prevalence,y=QSeq0.5, col=log(mean_abundance)))+
  geom_point()+ 
  scale_color_viridis_c(option="C")+
  theme_classic()

ggplot(model$model$SpeciesMeta, aes(x=prevalence,y=QSeq1, col=log(mean_abundance)))+
  geom_point()+ 
  scale_color_viridis_c(option="C")+
  theme_classic()

ggplot(model$model$SpeciesMeta, aes(x=prevalence,y=QSeq10, col=log(mean_abundance)))+
  geom_point()+ 
  scale_color_viridis_c(option="C")+
  theme_classic()

ggplot(model$model$SpeciesMeta, aes(x=prevalence,y=QSeq100, col=log(mean_abundance)))+
  geom_point()+ 
  scale_color_viridis_c(option="C")+
  theme_classic()

ggplot(model$model$SpeciesMeta, aes(x=log(mean_abundance),y=QSeq0.5, col=log(prevalence)))+
  geom_point()+ 
  scale_color_viridis_c(option="C")+
  theme_classic()

We can see that taxa that have higher prevalence also tend to retain more information; the one caveat is the taxa that exist in only one site. As long as they are detected, they retain perfect information.

We can explore to see how well species abundance and prevalence explain the LII:

summary(lm(model$model$SpeciesMeta$QSeq0.5~model$model$SpeciesMeta$prevalence*log(model$model$SpeciesMeta$mean_abundance)))

## 
## Call:
## lm(formula = model$model$SpeciesMeta$QSeq0.5 ~ model$model$SpeciesMeta$prevalence * 
##     log(model$model$SpeciesMeta$mean_abundance))
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.50230 -0.21672 -0.05508  0.15703  0.72949 
## 
## Coefficients:
##                                                                                 Estimate
## (Intercept)                                                                    -0.467800
## model$model$SpeciesMeta$prevalence                                             -0.004668
## log(model$model$SpeciesMeta$mean_abundance)                                    -0.085972
## model$model$SpeciesMeta$prevalence:log(model$model$SpeciesMeta$mean_abundance) -0.005053
##                                                                                Std. Error
## (Intercept)                                                                      0.136438
## model$model$SpeciesMeta$prevalence                                               0.010661
## log(model$model$SpeciesMeta$mean_abundance)                                      0.017884
## model$model$SpeciesMeta$prevalence:log(model$model$SpeciesMeta$mean_abundance)   0.001797
##                                                                                t value
## (Intercept)                                                                     -3.429
## model$model$SpeciesMeta$prevalence                                              -0.438
## log(model$model$SpeciesMeta$mean_abundance)                                     -4.807
## model$model$SpeciesMeta$prevalence:log(model$model$SpeciesMeta$mean_abundance)  -2.812
##                                                                                Pr(>|t|)
## (Intercept)                                                                    0.000824
## model$model$SpeciesMeta$prevalence                                             0.662241
## log(model$model$SpeciesMeta$mean_abundance)                                    4.34e-06
## model$model$SpeciesMeta$prevalence:log(model$model$SpeciesMeta$mean_abundance) 0.005729
##                                                                                   
## (Intercept)                                                                    ***
## model$model$SpeciesMeta$prevalence                                                
## log(model$model$SpeciesMeta$mean_abundance)                                    ***
## model$model$SpeciesMeta$prevalence:log(model$model$SpeciesMeta$mean_abundance) ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2905 on 124 degrees of freedom
## Multiple R-squared:  0.3896, Adjusted R-squared:  0.3748 
## F-statistic: 26.38 on 3 and 124 DF,  p-value: 2.889e-13

# look at prediction of prevalence
summary(lm(model$model$SpeciesMeta$QSeq0.5~model$model$SpeciesMeta$prevalence*log(model$model$SpeciesMeta$mean_abundance)))

## 
## Call:
## lm(formula = model$model$SpeciesMeta$QSeq0.5 ~ model$model$SpeciesMeta$prevalence * 
##     log(model$model$SpeciesMeta$mean_abundance))
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.50230 -0.21672 -0.05508  0.15703  0.72949 
## 
## Coefficients:
##                                                                                 Estimate
## (Intercept)                                                                    -0.467800
## model$model$SpeciesMeta$prevalence                                             -0.004668
## log(model$model$SpeciesMeta$mean_abundance)                                    -0.085972
## model$model$SpeciesMeta$prevalence:log(model$model$SpeciesMeta$mean_abundance) -0.005053
##                                                                                Std. Error
## (Intercept)                                                                      0.136438
## model$model$SpeciesMeta$prevalence                                               0.010661
## log(model$model$SpeciesMeta$mean_abundance)                                      0.017884
## model$model$SpeciesMeta$prevalence:log(model$model$SpeciesMeta$mean_abundance)   0.001797
##                                                                                t value
## (Intercept)                                                                     -3.429
## model$model$SpeciesMeta$prevalence                                              -0.438
## log(model$model$SpeciesMeta$mean_abundance)                                     -4.807
## model$model$SpeciesMeta$prevalence:log(model$model$SpeciesMeta$mean_abundance)  -2.812
##                                                                                Pr(>|t|)
## (Intercept)                                                                    0.000824
## model$model$SpeciesMeta$prevalence                                             0.662241
## log(model$model$SpeciesMeta$mean_abundance)                                    4.34e-06
## model$model$SpeciesMeta$prevalence:log(model$model$SpeciesMeta$mean_abundance) 0.005729
##                                                                                   
## (Intercept)                                                                    ***
## model$model$SpeciesMeta$prevalence                                                
## log(model$model$SpeciesMeta$mean_abundance)                                    ***
## model$model$SpeciesMeta$prevalence:log(model$model$SpeciesMeta$mean_abundance) ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2905 on 124 degrees of freedom
## Multiple R-squared:  0.3896, Adjusted R-squared:  0.3748 
## F-statistic: 26.38 on 3 and 124 DF,  p-value: 2.889e-13

summary(lm(model$model$SpeciesMeta$QSeq100~model$model$SpeciesMeta$prevalence*log(model$model$SpeciesMeta$mean_abundance)))

## 
## Call:
## lm(formula = model$model$SpeciesMeta$QSeq100 ~ model$model$SpeciesMeta$prevalence * 
##     log(model$model$SpeciesMeta$mean_abundance))
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.51005 -0.13549 -0.06243  0.09806  0.73822 
## 
## Coefficients:
##                                                                                 Estimate
## (Intercept)                                                                    -0.141802
## model$model$SpeciesMeta$prevalence                                             -0.019523
## log(model$model$SpeciesMeta$mean_abundance)                                    -0.028830
## model$model$SpeciesMeta$prevalence:log(model$model$SpeciesMeta$mean_abundance) -0.007697
##                                                                                Std. Error
## (Intercept)                                                                      0.105990
## model$model$SpeciesMeta$prevalence                                               0.008281
## log(model$model$SpeciesMeta$mean_abundance)                                      0.013893
## model$model$SpeciesMeta$prevalence:log(model$model$SpeciesMeta$mean_abundance)   0.001396
##                                                                                t value
## (Intercept)                                                                     -1.338
## model$model$SpeciesMeta$prevalence                                              -2.357
## log(model$model$SpeciesMeta$mean_abundance)                                     -2.075
## model$model$SpeciesMeta$prevalence:log(model$model$SpeciesMeta$mean_abundance)  -5.513
##                                                                                Pr(>|t|)
## (Intercept)                                                                       0.183
## model$model$SpeciesMeta$prevalence                                                0.020
## log(model$model$SpeciesMeta$mean_abundance)                                       0.040
## model$model$SpeciesMeta$prevalence:log(model$model$SpeciesMeta$mean_abundance) 1.95e-07
##                                                                                   
## (Intercept)                                                                       
## model$model$SpeciesMeta$prevalence                                             *  
## log(model$model$SpeciesMeta$mean_abundance)                                    *  
## model$model$SpeciesMeta$prevalence:log(model$model$SpeciesMeta$mean_abundance) ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2257 on 124 degrees of freedom
## Multiple R-squared:  0.462,  Adjusted R-squared:  0.449 
## F-statistic:  35.5 on 3 and 124 DF,  p-value: < 2.2e-16

Pay close attention to the R-squared values of the model. We can see that the prevalence and mean abundance explain the highest amount of variance in the LII model. This doesn’t necessarily mean that this model performs better; imagine if the relative patterns of all taxa are perfectly preserved, then there would be no relationship between the mean abundance, prevalence and information that is lost through sampling. Conversely, if we have a really high predictive power between the abundance, prevalence, and lost information, it doesn’t necessarily mean that the normalization is creating more bias in the dataset as there are likely real effects of relative abundance on the likelihood of detection in subsampling. This is to say that the statistics and the plots should be examined within the context of how the normalization procedure is known to operate in order to determine if it is creating bias. In this instance, QSeq0.5 decreases the R-squared of the model because some taxa are rounded down to 0, creating an anomaly that is removed at QSeq10 and QSeq100.

A note about lmRatio and lmRatio.model: As a reminder, the lmRatio and lmRatio.model values are the ratio of r-squared values of a model using normalized versus reference count tables. lmRatio is a model that regresses taxa against the environmental variables; lmRatio.model is a model that regresses taxa against the categorical experimental condition. values of 1 are interpreted to be a perfect retention of relationship through sampling and normalization; values between 0 and 1 are underestimation of the strength of the relationship; values over 1 are overestimation. So, let’s look at how mean abundance relates to accuracy of the linear model on a taxon-by-taxon basis:

plot(log(model$model$SpeciesMeta$mean_abundance),model$QSeq0.5$lmRatiotab, col=gray(model$model$SpeciesMeta$M.Eval), 
  main="QSeq0.5 R-ratio of Taxa vs Environment", xlab="Taxon Prevalence", ylab="R-Ratio")

plot(log(model$model$SpeciesMeta$mean_abundance),model$QSeq100$lmRatiotab, col=gray(model$model$SpeciesMeta$M.Eval), 
  main="QSeq100 R-ratio of Taxa vs Environment", xlab="Taxon Prevalence", ylab="R-Ratio")

Notice that QSeq0.5 has many more taxa that have completely lost the relationship between taxa and the environment, and a few where the relationship is over estimated. QSeq100 has none that have lost their relationship completely. While QSeq has more taxa that have an over-estimated relationship with the environmental variable, the accuracy of the estimate is still high, with most of those taxa still being within 10% error. Here is the same plots but for the categorical variables:

plot(log(model$model$SpeciesMeta$mean_abundance),model$QSeq0.5$lmRatiotab.model, col=gray(model$model$SpeciesMeta$M.Eval), 
   main="QSeq0.5 R-ratio of Taxa vs Category", xlab="Taxon Prevalence", ylab="R-Ratio")

plot(log(model$model$SpeciesMeta$mean_abundance),model$QSeq100$lmRatiotab.model, col=gray(model$model$SpeciesMeta$M.Eval), 
   main="QSeq100 R-ratio of Taxa vs Category", xlab="Taxon Prevalence", ylab="R-Ratio")

We can clearly see from both linear model R-Ratio plots that there are a number of taxa for which we lost completely any relationship. These were likely taxa that were rounded out of the community in QSeq0.5 but not QSeq100. We can also see that overall the general pattern of relationships is maintained across the rest of the taxa. The rate of overestimation of the relationship between taxa and explanitory variables also remains the same

You may notice that certain taxa have an R squared of 0; some of them improve as we increase the overall scaling factor. This happens when taxa are very low abundance in a particular sample. If their count abundance is less than 0.5, they get rounded down to 0. So ideally we want to pick a scaling value that lets us keep all the information from sampling (i.e. such that in all samples, the minimum taxon has a count of at least 1). This is an important observation if we want to use this method on a real dataset because it gives us a criteria for choosing what our scaling factor will be.

We can see qualitatively that our higher QSeq methods increase the accuracy of our taxon-specific models by a small margin. We can evaluate this statistically:

levenetest<-data.frame("ratio"=c(model$QSeq0.5$lmRatiotab, model$QSeq100$lmRatiotab), "method"=c(rep("raw", length(model$raw$lmRatiotab)), rep("QSeq", length(model$QSeq3$lmRatiotab))))

car::leveneTest(ratio ~ method, data = levenetest)

## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value  Pr(>F)  
## group   1  4.4617 0.03564 *
##       254                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

var(model$QSeq0.5$lmRatiotab)

## [1] 0.1127676

var(model$QSeq100$lmRatiotab)

## [1] 0.06331075

This indicates that there is greater variation in the lmRatio values in the QSeq0.5 versus the QSeq100. Remember, that the deviation in value from 1 represents lost accuracy in the information being retained; we can therefore interpret higher variance as being lower accuracy in the relationships being modeled after the transformation. This method provides a solid evidence-based approach for optimizing normalization methods.

It might be instructional at this point to look at the same distribution without any normalization, to see how well the normalization improves our inference about the relationship of taxa to their environment:

plot(model$model$SpeciesMeta$prevalence,model$raw$lmRatiotab, col=gray(model$model$SpeciesMeta$M.Eval), 
  main="Not normalized vs Environment", xlab="Taxon Prevalence", ylab="Rsquared-Ratio")

plot(model$model$SpeciesMeta$prevalence,model$QSeq100$lmRatiotab, col=gray(model$model$SpeciesMeta$M.Eval), 
  main="QSeq100 vs Environment", xlab="Taxon Prevalence", ylab="Rsquared-Ratio")

plot(model$model$SpeciesMeta$prevalence,model$raw$lmRatiotab.model, col=gray(model$model$SpeciesMeta$M.Eval), 
  main="Not normalized vs Category", xlab="Taxon Prevalence", ylab="Rsquared-Ratio")

plot(model$model$SpeciesMeta$prevalence,model$QSeq100$lmRatiotab.model, col=gray(model$model$SpeciesMeta$M.Eval), 
  main="QSeq100 vs Category", xlab="Taxon Prevalence", ylab="Rsquared-Ratio")

We can see that sometimes the differences are subtle, but other times normalization can remove large artifacts.

Now let’s look at how relationships among taxa are affected by normalization (or lack therof). We can access the R-Ratio for a correlation among taxa. Typically the first thing that we do for a network analysis is to correlate taxa to one another. Model.Microbiome does this automatically, using a pearson correlation. All we need to do is access this information using the getTaxCor.Tab function. This function outputs an object that contains a table of variances and median correlation ratios. These are calculated in a similar fashion as the correlation ratios of taxa to the environment;

let a be the correlation coefficient between two taxa in the reference. let b be the correlation coefficient between two taxa after normalization treatment.

The correlation ratio is defined as b/a

NOTE: because occasionally a = 0, resulting in an undefined result we have chosen to convert all a = 0 -> a = min(a/10) in order to remove infinite values, retain the information that these instances result in mis-estimation of the relationship between taxa, and without punishing the misestimation too harshly (an infinite value pushes the mean to infinite, even if only one infinite value exists in the dataset)

Thus we are extracting the variance of all ratios for each normalization method; and the median ratio of all normalization methods

model$raw$taxCor.Ratio

##         Var1   Var2         value
## 1     spp101 spp101  1.000000e+00
## 2     spp103 spp101  5.419079e-01
## 3     spp104 spp101  8.421576e-01
## 4     spp110 spp101  8.421576e-01
## 5     spp114 spp101 -9.531800e+00
## 6     spp116 spp101  8.421576e-01
## 7     spp126 spp101  5.420756e-02
## 8     spp133 spp101  5.438753e-01
## 9     spp139 spp101  7.187863e-01
## 10    spp152 spp101  6.020929e-01
## 11    spp165 spp101  6.457355e-01
## 12    spp168 spp101  7.081003e-01
## 13    spp169 spp101  1.027350e+00
## 14    spp177 spp101  1.772151e+00
## 15    spp185 spp101  5.972171e-01
## 16      spp2 spp101  6.856194e-01
## 17    spp204 spp101  7.121531e-01
## 18    spp209 spp101  7.092280e-01
## 19     spp21 spp101  5.034817e-01
## 20    spp216 spp101  5.823785e-01
## 21     spp22 spp101  6.832585e-01
## 22    spp220 spp101  8.421576e-01
## 23    spp231 spp101  8.421576e-01
## 24    spp232 spp101  8.421576e-01
## 25    spp238 spp101  8.421576e-01
## 26    spp243 spp101  2.880587e-01
## 27    spp251 spp101  6.061929e-01
## 28    spp252 spp101  8.541317e-01
## 29    spp253 spp101  8.421576e-01
## 30    spp256 spp101  6.740636e-01
## 31    spp257 spp101  6.473767e-01
## 32    spp259 spp101  8.421576e-01
## 33    spp267 spp101  9.711193e-01
## 34     spp27 spp101  8.421576e-01
## 35    spp271 spp101  7.138182e-01
## 36    spp272 spp101  8.421576e-01
## 37    spp273 spp101  6.879661e-01
## 38    spp279 spp101  4.982060e-01
## 39    spp285 spp101  4.731564e-01
## 40    spp286 spp101  8.421576e-01
## 41    spp290 spp101  1.070465e+00
## 42    spp293 spp101  4.982060e-01
## 43    spp296 spp101 -1.664746e-01
## 44    spp301 spp101  6.004743e-01
## 45    spp305 spp101  8.421576e-01
## 46    spp306 spp101  6.750509e-01
## 47    spp308 spp101  1.724700e+00
## 48    spp310 spp101  7.994843e-01
## 49    spp316 spp101  8.421576e-01
## 50    spp319 spp101  7.358415e-01
## 51     spp32 spp101  7.473883e-01
## 52    spp329 spp101  4.268185e-01
## 53     spp33 spp101  4.966536e-01
## 54    spp332 spp101  8.421576e-01
## 55    spp337 spp101  6.552562e-01
## 56    spp339 spp101  8.421576e-01
## 57    spp340 spp101  6.756354e-01
## 58    spp344 spp101  8.795363e-02
## 59    spp349 spp101  8.421576e-01
## 60    spp353 spp101  8.421576e-01
## 61    spp354 spp101  7.401367e-01
## 62     spp36 spp101  5.420188e-01
## 63    spp362 spp101  7.263913e-01
## 64    spp366 spp101  7.408176e-01
## 65    spp370 spp101  8.977445e-01
## 66    spp373 spp101  8.421576e-01
## 67    spp375 spp101  8.421576e-01
## 68    spp380 spp101  8.421576e-01
## 69    spp381 spp101  1.005913e+00
## 70    spp384 spp101  6.546863e-01
## 71    spp386 spp101  8.643989e-01
## 72    spp387 spp101  7.303813e-01
## 73    spp388 spp101  8.421576e-01
## 74    spp389 spp101  8.063377e-01
## 75    spp392 spp101  1.170364e+00
## 76    spp393 spp101  9.293574e-01
## 77    spp394 spp101  6.905865e-01
## 78    spp395 spp101  8.421576e-01
## 79    spp398 spp101  8.421576e-01
## 80      spp4 spp101  8.421576e-01
## 81     spp40 spp101  5.679842e-01
## 82    spp406 spp101  8.808432e-01
## 83    spp407 spp101  9.520397e-01
## 84    spp410 spp101  8.421576e-01
## 85    spp416 spp101  7.040233e-01
## 86    spp418 spp101  3.593440e-01
## 87    spp421 spp101  4.592971e-01
## 88    spp439 spp101  1.200846e-01
## 89    spp457 spp101  8.421576e-01
## 90    spp459 spp101  7.381811e-01
## 91    spp467 spp101  1.028389e+00
## 92    spp469 spp101  9.343638e-01
## 93    spp475 spp101  3.837656e-01
## 94    spp481 spp101  5.823814e-01
## 95    spp483 spp101  4.917741e-01
## 96    spp490 spp101  9.206078e-01
## 97    spp492 spp101  8.411929e-01
## 98    spp501 spp101  9.020396e-01
## 99    spp503 spp101  7.308994e-01
## 100    spp51 spp101  8.421576e-01
## 101   spp514 spp101  7.269156e-01
## 102   spp515 spp101  1.887819e-01
## 103   spp519 spp101  5.446328e-01
## 104   spp521 spp101  1.014201e+00
## 105   spp527 spp101  6.259040e-01
## 106   spp537 spp101  2.553234e-01
## 107   spp547 spp101  4.801151e-01
## 108   spp555 spp101  8.486684e-01
## 109   spp559 spp101 -8.351875e+00
## 110   spp565 spp101  8.421576e-01
## 111   spp567 spp101  5.420756e-02
## 112   spp569 spp101  9.460648e-01
## 113    spp59 spp101  7.205076e-01
## 114     spp6 spp101  8.421576e-01
## 115    spp60 spp101  7.476396e-01
## 116   spp601 spp101  6.266669e-01
## 117   spp604 spp101  1.032418e+00
## 118    spp62 spp101  6.326916e-01
## 119   spp634 spp101  5.117990e-02
## 120   spp639 spp101  5.199854e-01
## 121   spp653 spp101  8.421576e-01
## 122   spp654 spp101  6.857520e-01
## 123   spp659 spp101  8.421576e-01
## 124   spp668 spp101  8.421576e-01
## 125   spp679 spp101  1.270305e+00
## 126   spp684 spp101  8.332113e-01
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## 1826   spp27 spp185  7.091512e-01
## 1827  spp271 spp185 -5.786092e-01
## 1828  spp272 spp185  2.522901e+00
## 1829  spp273 spp185 -6.446766e-01
## 1830  spp279 spp185  7.091512e-01
## 1831  spp285 spp185  5.132025e-01
## 1832  spp286 spp185  7.091512e-01
## 1833  spp290 spp185  2.093682e-01
## 1834  spp293 spp185  7.091512e-01
## 1835  spp296 spp185  1.532113e+00
## 1836  spp301 spp185 -9.052314e-02
## 1837  spp305 spp185  7.091512e-01
## 1838  spp306 spp185  5.684366e-01
## 1839  spp308 spp185  7.091512e-01
## 1840  spp310 spp185  8.951394e-01
## 1841  spp316 spp185  7.091512e-01
## 1842  spp319 spp185  6.196262e-01
## 1843   spp32 spp185  6.293494e-01
## 1844  spp329 spp185  2.910808e-01
## 1845   spp33 spp185  4.182145e-01
## 1846  spp332 spp185  7.091512e-01
## 1847  spp337 spp185  1.983709e+00
## 1848  spp339 spp185  7.091512e-01
## 1849  spp340 spp185  1.314768e+00
## 1850  spp344 spp185  2.933406e+00
## 1851  spp349 spp185  5.917334e-01
## 1852  spp353 spp185  7.091512e-01
## 1853  spp354 spp185  6.232430e-01
## 1854   spp36 spp185  4.564149e-01
## 1855  spp362 spp185  6.116685e-01
## 1856  spp366 spp185  6.238164e-01
## 1857  spp370 spp185  7.559590e-01
## 1858  spp373 spp185  7.091512e-01
## 1859  spp375 spp185  7.091512e-01
## 1860  spp380 spp185  7.091512e-01
## 1861  spp381 spp185  6.038548e-01
## 1862  spp384 spp185  6.059951e-01
## 1863  spp386 spp185  8.208256e-01
## 1864  spp387 spp185  6.150283e-01
## 1865  spp388 spp185  7.091512e-01
## 1866  spp389 spp185  1.451747e-02
## 1867  spp392 spp185  6.598036e-01
## 1868  spp393 spp185  6.688119e-01
## 1869  spp394 spp185  5.815186e-01
## 1870  spp395 spp185  7.091512e-01
## 1871  spp398 spp185  7.091512e-01
## 1872    spp4 spp185  7.091512e-01
## 1873   spp40 spp185  2.731407e-01
## 1874  spp406 spp185  7.044600e-01
## 1875  spp407 spp185  8.016791e-01
## 1876  spp410 spp185  7.091512e-01
## 1877  spp416 spp185  5.928332e-01
## 1878  spp418 spp185  3.025909e-01
## 1879  spp421 spp185  3.867579e-01
## 1880  spp439 spp185 -1.857868e-01
## 1881  spp457 spp185  5.917334e-01
## 1882  spp459 spp185  6.215963e-01
## 1883  spp467 spp185  6.037087e-01
## 1884  spp469 spp185  1.034367e+00
## 1885  spp475 spp185  3.231555e-01
## 1886  spp481 spp185  4.904029e-01
## 1887  spp483 spp185  4.141056e-01
## 1888  spp490 spp185  4.455326e-01
## 1889  spp492 spp185  5.262410e-01
## 1890  spp501 spp185  7.595757e-01
## 1891  spp503 spp185  6.154646e-01
## 1892   spp51 spp185  7.091512e-01
## 1893  spp514 spp185 -1.444902e+00
## 1894  spp515 spp185 -1.936397e+00
## 1895  spp519 spp185 -1.023232e-01
## 1896  spp521 spp185  3.782756e+00
## 1897  spp527 spp185 -4.665067e-01
## 1898  spp537 spp185 -3.902267e-01
## 1899  spp547 spp185  4.042880e-01
## 1900  spp555 spp185 -7.374103e-01
## 1901  spp559 spp185  6.533231e-01
## 1902  spp565 spp185  2.968388e-01
## 1903  spp567 spp185  7.091512e-01
## 1904  spp569 spp185  6.787667e-01
## 1905   spp59 spp185  6.067140e-01
## 1906    spp6 spp185  7.091512e-01
## 1907   spp60 spp185  6.295610e-01
## 1908  spp601 spp185  5.276941e-01
## 1909  spp604 spp185  8.693630e-01
## 1910   spp62 spp185 -1.066044e+00
## 1911  spp634 spp185 -8.505122e-01
## 1912  spp639 spp185  4.378614e-01
## 1913  spp653 spp185  7.091512e-01
## 1914  spp654 spp185  5.774476e-01
## 1915  spp659 spp185  7.091512e-01
## 1916  spp668 spp185  7.091512e-01
## 1917  spp679 spp185  4.971531e-01
## 1918  spp684 spp185  1.081030e+00
## 1919   spp85 spp185  1.363623e+00
## 1920    spp9 spp185  5.849145e-01
## 1921  spp101   spp2  6.856194e-01
## 1922  spp103   spp2  2.578335e+00
## 1923  spp104   spp2  8.141224e-01
## 1924  spp110   spp2  8.141224e-01
## 1925  spp114   spp2  3.431231e-01
## 1926  spp116   spp2  5.965961e-01
## 1927  spp126   spp2  8.141224e-01
## 1928  spp133   spp2  9.433188e-01
## 1929  spp139   spp2  6.948581e-01
## 1930  spp152   spp2  5.820494e-01
## 1931  spp165   spp2  3.198744e-01
## 1932  spp168   spp2  5.962455e-01
## 1933  spp169   spp2  2.428694e-01
## 1934  spp177   spp2 -4.890384e-01
## 1935  spp185   spp2  5.773359e-01
## 1936    spp2   spp2  1.000000e+00
## 1937  spp204   spp2  2.503374e-01
## 1938  spp209   spp2  8.405212e-01
## 1939   spp21   spp2  4.867210e-01
## 1940  spp216   spp2  5.629913e-01
## 1941   spp22   spp2  5.702325e-01
## 1942  spp220   spp2  8.141224e-01
## 1943  spp231   spp2  1.869828e+00
## 1944  spp232   spp2  8.141224e-01
## 1945  spp238   spp2  8.141224e-01
## 1946  spp243   spp2  3.905451e-01
## 1947  spp251   spp2  1.040346e+00
## 1948  spp252   spp2  8.256979e-01
## 1949  spp253   spp2  8.141224e-01
## 1950  spp256   spp2  6.516243e-01
## 1951  spp257   spp2  6.258258e-01
## 1952  spp259   spp2  8.141224e-01
## 1953  spp267   spp2 -1.604909e-01
## 1954   spp27   spp2  8.141224e-01
## 1955  spp271   spp2  8.522017e-01
## 1956  spp272   spp2  8.141224e-01
## 1957  spp273   spp2 -1.358229e-01
## 1958  spp279   spp2  8.141224e-01
## 1959  spp285   spp2  5.891686e-01
## 1960  spp286   spp2  8.141224e-01
## 1961  spp290   spp2  1.034830e+00
## 1962  spp293   spp2  8.141224e-01
## 1963  spp296   spp2  2.959817e-01
## 1964  spp301   spp2  5.804847e-01
## 1965  spp305   spp2  7.732503e-01
## 1966  spp306   spp2  6.525787e-01
## 1967  spp308   spp2  8.141224e-01
## 1968  spp310   spp2  7.728698e-01
## 1969  spp316   spp2  1.869828e+00
## 1970  spp319   spp2  7.113456e-01
## 1971   spp32   spp2  9.651910e-01
## 1972  spp329   spp2  3.616522e+00
## 1973   spp33   spp2  4.801202e-01
## 1974  spp332   spp2  8.141224e-01
## 1975  spp337   spp2 -8.833676e-01
## 1976  spp339   spp2  1.557749e-01
## 1977  spp340   spp2 -2.591146e+00
## 1978  spp344   spp2  9.154428e-01
## 1979  spp349   spp2  8.141224e-01
## 1980  spp353   spp2  8.141224e-01
## 1981  spp354   spp2  1.021928e+00
## 1982   spp36   spp2  5.239752e-01
## 1983  spp362   spp2  7.022100e-01
## 1984  spp366   spp2  7.161561e-01
## 1985  spp370   spp2  8.678589e-01
## 1986  spp373   spp2  8.141224e-01
## 1987  spp375   spp2  8.141224e-01
## 1988  spp380   spp2  5.965961e-01
## 1989  spp381   spp2  6.932396e-01
## 1990  spp384   spp2  4.426585e+00
## 1991  spp386   spp2  8.356233e-01
## 1992  spp387   spp2  9.988755e-01
## 1993  spp388   spp2  1.869828e+00
## 1994  spp389   spp2  1.767362e+01
## 1995  spp392   spp2  7.574702e-01
## 1996  spp393   spp2  7.678119e-01
## 1997  spp394   spp2  6.675971e-01
## 1998  spp395   spp2  5.965961e-01
## 1999  spp398   spp2  8.141224e-01
## 2000    spp4   spp2  6.022663e-01
## 2001   spp40   spp2  5.490762e-01
## 2002  spp406   spp2  8.087368e-01
## 2003  spp407   spp2  9.203466e-01
## 2004  spp410   spp2  8.141224e-01
## 2005  spp416   spp2  6.805866e-01
## 2006  spp418   spp2  4.853933e-01
## 2007  spp421   spp2  1.226174e-01
## 2008  spp439   spp2  2.994753e+00
## 2009  spp457   spp2  8.141224e-01
## 2010  spp459   spp2  1.009165e+00
## 2011  spp467   spp2  6.930719e-01
## 2012  spp469   spp2  3.469275e-01
## 2013  spp475   spp2  3.709902e-01
## 2014  spp481   spp2  7.445190e-01
## 2015  spp483   spp2  4.754031e-01
## 2016  spp490   spp2  5.114820e-01
## 2017  spp492   spp2  6.041372e-01
## 2018  spp501   spp2  8.720110e-01
## 2019  spp503   spp2  4.288378e-01
## 2020   spp51   spp2  6.022663e-01
## 2021  spp514   spp2  7.407820e-01
## 2022  spp515   spp2  2.667565e+00
## 2023  spp519   spp2  5.265021e-01
## 2024  spp521   spp2  5.922980e-01
## 2025  spp527   spp2  7.296308e-01
## 2026  spp537   spp2  3.339075e+00
## 2027  spp547   spp2  1.666475e-01
## 2028  spp555   spp2  8.204165e-01
## 2029  spp559   spp2  7.500305e-01
## 2030  spp565   spp2  8.141224e-01
## 2031  spp567   spp2  8.141224e-01
## 2032  spp569   spp2  7.792403e-01
## 2033   spp59   spp2  1.285832e+00
## 2034    spp6   spp2  8.141224e-01
## 2035   spp60   spp2  7.227509e-01
## 2036  spp601   spp2  6.058054e-01
## 2037  spp604   spp2  9.980494e-01
## 2038   spp62   spp2  3.414473e+00
## 2039  spp634   spp2  2.458505e+00
## 2040  spp639   spp2  9.010513e-01
## 2041  spp653   spp2  7.732503e-01
## 2042  spp654   spp2  1.027353e+00
## 2043  spp659   spp2  8.141224e-01
## 2044  spp668   spp2  8.141224e-01
## 2045  spp679   spp2  5.707436e-01
## 2046  spp684   spp2 -1.048417e-01
## 2047   spp85   spp2 -1.198565e+00
## 2048    spp9   spp2  9.868882e-01
## 2049  spp101 spp204  7.121531e-01
## 2050  spp103 spp204  6.371383e-01
## 2051  spp104 spp204  8.456293e-01
## 2052  spp110 spp204  8.456293e-01
## 2053  spp114 spp204  3.564021e-01
## 2054  spp116 spp204  6.613596e-01
## 2055  spp126 spp204  8.456293e-01
## 2056  spp133 spp204  1.209099e-01
## 2057  spp139 spp204  7.217494e-01
## 2058  spp152 spp204  6.045750e-01
## 2059  spp165 spp204  2.591236e-01
## 2060  spp168 spp204  3.885247e-01
## 2061  spp169 spp204  1.169931e+00
## 2062  spp177 spp204  2.155754e-01
## 2063  spp185 spp204  5.996790e-01
## 2064    spp2 spp204  2.503374e-01
## 2065  spp204 spp204  1.000000e+00
## 2066  spp209 spp204  5.994532e-02
## 2067   spp21 spp204  5.055573e-01
## 2068  spp216 spp204  5.847793e-01
## 2069   spp22 spp204  8.410220e-01
## 2070  spp220 spp204  8.456293e-01
## 2071  spp231 spp204  8.456293e-01
## 2072  spp232 spp204  8.456293e-01
## 2073  spp238 spp204  8.456293e-01
## 2074  spp243 spp204  4.056593e-01
## 2075  spp251 spp204  1.471540e-01
## 2076  spp252 spp204  8.576528e-01
## 2077  spp253 spp204  8.456293e-01
## 2078  spp256 spp204  6.768424e-01
## 2079  spp257 spp204  6.500455e-01
## 2080  spp259 spp204  8.456293e-01
## 2081  spp267 spp204  9.066095e-01
## 2082   spp27 spp204  8.456293e-01
## 2083  spp271 spp204  9.035173e-01
## 2084  spp272 spp204  8.456293e-01
## 2085  spp273 spp204 -1.790718e+00
## 2086  spp279 spp204  8.456293e-01
## 2087  spp285 spp204  6.119697e-01
## 2088  spp286 spp204  8.456293e-01
## 2089  spp290 spp204  1.074878e+00
## 2090  spp293 spp204  8.456293e-01
## 2091  spp296 spp204  3.074363e-01
## 2092  spp301 spp204  6.029497e-01
## 2093  spp305 spp204  2.122970e-01
## 2094  spp306 spp204  6.778338e-01
## 2095  spp308 spp204  8.456293e-01
## 2096  spp310 spp204  8.027802e-01
## 2097  spp316 spp204  8.456293e-01
## 2098  spp319 spp204  7.388750e-01
## 2099   spp32 spp204  2.215875e-01
## 2100  spp329 spp204  1.506058e+00
## 2101   spp33 spp204  4.987011e-01
## 2102  spp332 spp204  8.456293e-01
## 2103  spp337 spp204  8.372099e-02
## 2104  spp339 spp204  5.037202e-01
## 2105  spp340 spp204 -4.137729e-01
## 2106  spp344 spp204  7.214214e-01
## 2107  spp349 spp204  8.456293e-01
## 2108  spp353 spp204  8.456293e-01
## 2109  spp354 spp204  5.682873e-01
## 2110   spp36 spp204  5.442532e-01
## 2111  spp362 spp204  7.293858e-01
## 2112  spp366 spp204  7.438716e-01
## 2113  spp370 spp204  9.014454e-01
## 2114  spp373 spp204  8.456293e-01
## 2115  spp375 spp204  8.456293e-01
## 2116  spp380 spp204  6.613596e-01
## 2117  spp381 spp204  7.200683e-01
## 2118  spp384 spp204  1.781314e+00
## 2119  spp386 spp204  8.679623e-01
## 2120  spp387 spp204  4.813248e-01
## 2121  spp388 spp204  8.456293e-01
## 2122  spp389 spp204  8.654537e-01
## 2123  spp392 spp204  7.867847e-01
## 2124  spp393 spp204  7.975266e-01
## 2125  spp394 spp204  6.934334e-01
## 2126  spp395 spp204  6.613596e-01
## 2127  spp398 spp204  8.456293e-01
## 2128    spp4 spp204  1.660103e+00
## 2129   spp40 spp204  5.703256e-01
## 2130  spp406 spp204  8.400353e-01
## 2131  spp407 spp204  9.559644e-01
## 2132  spp410 spp204  8.456293e-01
## 2133  spp416 spp204  7.069256e-01
## 2134  spp418 spp204  2.617494e+00
## 2135  spp421 spp204  3.926485e-01
## 2136  spp439 spp204 -5.561687e-02
## 2137  spp457 spp204  8.456293e-01
## 2138  spp459 spp204  1.997246e-01
## 2139  spp467 spp204  7.198941e-01
## 2140  spp469 spp204  5.056683e-01
## 2141  spp475 spp204  3.853477e-01
## 2142  spp481 spp204  7.473418e-01
## 2143  spp483 spp204  4.938014e-01
## 2144  spp490 spp204  5.312766e-01
## 2145  spp492 spp204  6.275175e-01
## 2146  spp501 spp204  9.057582e-01
## 2147  spp503 spp204  1.347204e+00
## 2148   spp51 spp204  1.660103e+00
## 2149  spp514 spp204  7.694506e-01
## 2150  spp515 spp204 -4.211347e-01
## 2151  spp519 spp204  5.468780e-01
## 2152  spp521 spp204  6.152202e-01
## 2153  spp527 spp204  7.578678e-01
## 2154  spp537 spp204  4.880914e-01
## 2155  spp547 spp204  3.963398e-01
## 2156  spp555 spp204  8.521670e-01
## 2157  spp559 spp204  7.790570e-01
## 2158  spp565 spp204  8.456293e-01
## 2159  spp567 spp204  8.456293e-01
## 2160  spp569 spp204  8.093972e-01
## 2161   spp59 spp204 -1.856526e+00
## 2162    spp6 spp204  8.456293e-01
## 2163   spp60 spp204  7.507217e-01
## 2164  spp601 spp204  6.292503e-01
## 2165  spp604 spp204  1.036674e+00
## 2166   spp62 spp204  5.735718e+00
## 2167  spp634 spp204  1.922462e-01
## 2168  spp639 spp204  1.334221e-01
## 2169  spp653 spp204  2.122970e-01
## 2170  spp654 spp204  4.097715e-01
## 2171  spp659 spp204  8.456293e-01
## 2172  spp668 spp204  8.456293e-01
## 2173  spp679 spp204  5.928316e-01
## 2174  spp684 spp204  1.046441e+00
## 2175   spp85 spp204  5.154755e-01
## 2176    spp9 spp204  3.156557e-01
## 2177  spp101 spp209  7.092280e-01
## 2178  spp103 spp209  3.030311e+00
## 2179  spp104 spp209  8.421560e-01
## 2180  spp110 spp209  8.421560e-01
## 2181  spp114 spp209  3.714177e-01
## 2182  spp116 spp209  8.421560e-01
## 2183  spp126 spp209  8.421560e-01
## 2184  spp133 spp209  6.525321e-02
## 2185  spp139 spp209  7.044966e-01
## 2186  spp152 spp209  6.546789e-01
## 2187  spp165 spp209  1.051059e+00
## 2188  spp168 spp209  2.245723e+00
## 2189  spp169 spp209  3.250488e-01
## 2190  spp177 spp209  6.149733e-01
## 2191  spp185 spp209  5.972159e-01
## 2192    spp2 spp209  8.405212e-01
## 2193  spp204 spp209  5.994532e-02
## 2194  spp209 spp209  1.000000e+00
## 2195   spp21 spp209  5.034808e-01
## 2196  spp216 spp209  6.074768e-01
## 2197   spp22 spp209  2.020690e-02
## 2198  spp220 spp209  8.421560e-01
## 2199  spp231 spp209  8.421560e-01
## 2200  spp232 spp209  8.421560e-01
## 2201  spp238 spp209  1.054754e+00
## 2202  spp243 spp209  4.039931e-01
## 2203  spp251 spp209  5.058337e-01
## 2204  spp252 spp209  8.541301e-01
## 2205  spp253 spp209  8.421560e-01
## 2206  spp256 spp209  6.740623e-01
## 2207  spp257 spp209  7.948189e-01
## 2208  spp259 spp209  8.421560e-01
## 2209  spp267 spp209 -5.409383e-01
## 2210   spp27 spp209  8.421560e-01
## 2211  spp271 spp209 -6.205613e-01
## 2212  spp272 spp209  8.421560e-01
## 2213  spp273 spp209 -3.805773e-01
## 2214  spp279 spp209  8.421560e-01
## 2215  spp285 spp209  6.094561e-01
## 2216  spp286 spp209  8.421560e-01
## 2217  spp290 spp209 -1.663966e+01
## 2218  spp293 spp209  8.421560e-01
## 2219  spp296 spp209  3.061736e-01
## 2220  spp301 spp209  6.004732e-01
## 2221  spp305 spp209  1.037673e+00
## 2222  spp306 spp209  6.808784e-01
## 2223  spp308 spp209  8.421560e-01
## 2224  spp310 spp209  7.994828e-01
## 2225  spp316 spp209  8.421560e-01
## 2226  spp319 spp209  7.307679e-01
## 2227   spp32 spp209  1.494716e+00
## 2228  spp329 spp209 -4.493956e+00
## 2229   spp33 spp209  6.363473e-01
## 2230  spp332 spp209  8.421560e-01
## 2231  spp337 spp209  2.051379e+00
## 2232  spp339 spp209  8.421560e-01
## 2233  spp340 spp209  2.279704e+00
## 2234  spp344 spp209  8.393057e-01
## 2235  spp349 spp209  8.421560e-01
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## 2237  spp354 spp209  1.180897e+00
## 2238   spp36 spp209  5.420178e-01
## 2239  spp362 spp209  7.263900e-01
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## 2241  spp370 spp209  8.977428e-01
## 2242  spp373 spp209 -5.772340e-02
## 2243  spp375 spp209 -6.321097e+00
## 2244  spp380 spp209  8.421560e-01
## 2245  spp381 spp209  7.171107e-01
## 2246  spp384 spp209 -3.251272e-01
## 2247  spp386 spp209  8.643972e-01
## 2248  spp387 spp209  8.204183e-01
## 2249  spp388 spp209  8.421560e-01
## 2250  spp389 spp209  4.717040e-01
## 2251  spp392 spp209  7.835530e-01
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## 2253  spp394 spp209  6.905852e-01
## 2254  spp395 spp209  8.421560e-01
## 2255  spp398 spp209  8.421560e-01
## 2256    spp4 spp209  8.421560e-01
## 2257   spp40 spp209  5.679831e-01
## 2258  spp406 spp209  8.365849e-01
## 2259  spp407 spp209  9.520379e-01
## 2260  spp410 spp209  8.421560e-01
## 2261  spp416 spp209  7.040220e-01
## 2262  spp418 spp209 -1.149634e+00
## 2263  spp421 spp209 -1.651665e-01
## 2264  spp439 spp209 -2.429778e+01
## 2265  spp457 spp209  8.421560e-01
## 2266  spp459 spp209  1.196486e+00
## 2267  spp467 spp209  7.404603e-01
## 2268  spp469 spp209  2.403047e-01
## 2269  spp475 spp209  3.837649e-01
## 2270  spp481 spp209 -2.459191e-01
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## 2280  spp521 spp209  6.126932e-01
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## 2288  spp569 spp209  8.060727e-01
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## 2291   spp60 spp209  7.476382e-01
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## 2293  spp604 spp209  1.032416e+00
## 2294   spp62 spp209 -6.375627e+00
## 2295  spp634 spp209 -6.728426e+01
## 2296  spp639 spp209 -2.587484e-01
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## 2299  spp659 spp209 -5.772340e-02
## 2300  spp668 spp209  1.054754e+00
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## 2302  spp684 spp209  6.080001e-01
## 2303   spp85 spp209  5.133582e-01
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## 2305  spp101  spp21  5.034817e-01
## 2306  spp103  spp21 -1.395390e-01
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## 2318  spp177  spp21 -1.221704e-01
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## 2321  spp204  spp21  5.055573e-01
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## 2336  spp259  spp21  2.466433e+00
## 2337  spp267  spp21  4.542584e-02
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## 2627  spp375  spp22 -2.577814e-01
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## 6394  spp654 spp319  7.114832e-01
## 6395  spp659 spp319 -4.546805e-02
## 6396  spp668 spp319  1.374890e+00
## 6397  spp679 spp319  6.125510e-01
## 6398  spp684 spp319  3.057296e-01
## 6399   spp85 spp319  5.326217e-01
## 6400    spp9 spp319  7.206834e-01
## 6401  spp101  spp32  7.473883e-01
## 6402  spp103  spp32  2.519430e+00
## 6403  spp104  spp32  8.874685e-01
## 6404  spp110  spp32  8.874685e-01
## 6405  spp114  spp32  3.740358e-01
## 6406  spp116  spp32  2.357191e+00
## 6407  spp126  spp32  8.874685e-01
## 6408  spp133  spp32  8.185072e-01
## 6409  spp139  spp32  7.574594e-01
## 6410  spp152  spp32  6.344876e-01
## 6411  spp165  spp32  6.496421e-01
## 6412  spp168  spp32  8.382800e-01
## 6413  spp169  spp32  2.439958e-01
## 6414  spp177  spp32 -6.517003e-01
## 6415  spp185  spp32  6.293494e-01
## 6416    spp2  spp32  9.651910e-01
## 6417  spp204  spp32  2.215875e-01
## 6418  spp209  spp32  1.494716e+00
## 6419   spp21  spp32  5.305708e-01
## 6420  spp216  spp32  6.137124e-01
## 6421   spp22  spp32  5.563666e-01
## 6422  spp220  spp32  8.874685e-01
## 6423  spp231  spp32  1.427005e+00
## 6424  spp232  spp32  8.874685e-01
## 6425  spp238  spp32  8.874685e-01
## 6426  spp243  spp32  4.257301e-01
## 6427  spp251  spp32  9.164944e-01
## 6428  spp252  spp32  9.000869e-01
## 6429  spp253  spp32  8.874685e-01
## 6430  spp256  spp32  7.103305e-01
## 6431  spp257  spp32  6.822078e-01
## 6432  spp259  spp32  8.874685e-01
## 6433  spp267  spp32 -2.573929e-01
## 6434   spp27  spp32  8.874685e-01
## 6435  spp271  spp32  8.098003e-01
## 6436  spp272  spp32  8.874685e-01
## 6437  spp273  spp32 -4.720071e-01
## 6438  spp279  spp32  8.874685e-01
## 6439  spp285  spp32  6.422481e-01
## 6440  spp286  spp32  8.874685e-01
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## 6443  spp296  spp32  3.226474e-01
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## 6445  spp305  spp32  1.288218e+00
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## 6447  spp308  spp32  8.874685e-01
## 6448  spp310  spp32  8.424993e-01
## 6449  spp316  spp32  1.427005e+00
## 6450  spp319  spp32  7.754323e-01
## 6451   spp32  spp32  1.000000e+00
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## 6455  spp337  spp32 -9.225492e-01
## 6456  spp339  spp32  5.108941e-02
## 6457  spp340  spp32 -2.199840e+00
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## 6460  spp353  spp32  8.874685e-01
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## 6464  spp366  spp32  7.806762e-01
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## 6470  spp384  spp32  3.846996e+00
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## 6478  spp395  spp32  2.357191e+00
## 6479  spp398  spp32  8.874685e-01
## 6480    spp4  spp32  2.133561e-01
## 6481   spp40  spp32  5.985437e-01
## 6482  spp406  spp32  8.815977e-01
## 6483  spp407  spp32  1.003263e+00
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## 6487  spp421  spp32  4.404275e-02
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## 6490  spp459  spp32  9.417681e-01
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## 6516  spp601  spp32  6.603837e-01
## 6517  spp604  spp32  1.087966e+00
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## 6519  spp634  spp32  2.140486e+00
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## 6527   spp85  spp32 -9.517943e-01
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## 6544    spp2 spp329  3.616522e+00
## 6545  spp204 spp329  1.506058e+00
## 6546  spp209 spp329 -4.493956e+00
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## 6548  spp216 spp329  2.884662e-01
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## 6550  spp220 spp329  2.395647e-01
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## 6553  spp238 spp329 -7.974998e-02
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## 6565  spp273 spp329  1.131128e-01
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## 6578  spp319 spp329  1.368667e-01
## 6579   spp32 spp329  3.283938e+00
## 6580  spp329 spp329  1.000000e+00
## 6581   spp33 spp329 -8.902612e-02
## 6582  spp332 spp329  4.694759e-01
## 6583  spp337 spp329 -4.198861e-01
## 6584  spp339 spp329  1.741892e-01
## 6585  spp340 spp329 -4.614098e+00
## 6586  spp344 spp329 -2.231484e+00
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## 6588  spp353 spp329 -4.696541e-01
## 6589  spp354 spp329  4.311707e+00
## 6590   spp36 spp329  4.130342e-01
## 6591  spp362 spp329  1.366057e-01
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## 6594  spp373 spp329  1.893443e+00
## 6595  spp375 spp329  4.515216e-01
## 6596  spp380 spp329 -6.304849e+00
## 6597  spp381 spp329  4.204733e-01
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## 6602  spp389 spp329  8.159037e-01
## 6603  spp392 spp329  1.526955e+00
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## 6605  spp394 spp329  5.784697e-01
## 6606  spp395 spp329 -6.304849e+00
## 6607  spp398 spp329  9.493489e-01
## 6608    spp4 spp329  3.532637e+00
## 6609   spp40 spp329  1.217925e-01
## 6610  spp406 spp329  6.104962e-01
## 6611  spp407 spp329  7.648434e-02
## 6612  spp410 spp329  1.551776e-01
## 6613  spp416 spp329  5.912408e-01
## 6614  spp418 spp329  2.554734e-01
## 6615  spp421 spp329  1.588294e-01
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## 6621  spp475 spp329 -3.212413e-01
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## 6640  spp569 spp329  5.288539e-01
## 6641   spp59 spp329  8.735884e-01
## 6642    spp6 spp329 -3.141875e-01
## 6643   spp60 spp329  1.424008e-01
## 6644  spp601 spp329  4.823581e-01
## 6645  spp604 spp329  3.986271e-02
## 6646   spp62 spp329  5.403627e-01
## 6647  spp634 spp329  9.693077e-01
## 6648  spp639 spp329  3.001853e+00
## 6649  spp653 spp329  4.259202e+00
## 6650  spp654 spp329  3.654001e+00
## 6651  spp659 spp329  1.893443e+00
## 6652  spp668 spp329 -7.974998e-02
## 6653  spp679 spp329  1.702517e-01
## 6654  spp684 spp329  4.104314e-01
## 6655   spp85 spp329  5.184265e-01
## 6656    spp9 spp329  3.635226e+00
## 6657  spp101  spp33  4.966536e-01
## 6658  spp103  spp33 -6.640161e-01
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## 6660  spp110  spp33  5.897396e-01
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## 6670  spp177  spp33  2.569941e-01
## 6671  spp185  spp33  4.182145e-01
## 6672    spp2  spp33  4.801202e-01
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## 6674  spp209  spp33  6.363473e-01
## 6675   spp21  spp33  3.525743e-01
## 6676  spp216  spp33  6.448343e-01
## 6677   spp22  spp33 -1.371224e-01
## 6678  spp220  spp33  5.897396e-01
## 6679  spp231  spp33  5.897396e-01
## 6680  spp232  spp33  5.897396e-01
## 6681  spp238  spp33 -9.261337e-02
## 6682  spp243  spp33  2.829057e-01
## 6683  spp251  spp33  4.245001e-01
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## 6686  spp256  spp33  4.720280e-01
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## 6691  spp271  spp33  4.998671e-01
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## 6693  spp273  spp33  3.192658e-01
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## 6702  spp306  spp33  1.139860e-01
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## 6704  spp310  spp33  5.598567e-01
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## 6706  spp319  spp33  6.950169e-01
## 6707   spp32  spp33  5.233753e-01
## 6708  spp329  spp33 -8.902612e-02
## 6709   spp33  spp33  1.000000e+00
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## 6719  spp362  spp33  5.086717e-01
## 6720  spp366  spp33  5.187740e-01
## 6721  spp370  spp33  6.286656e-01
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## 6726  spp384  spp33 -8.773510e-02
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## 6728  spp387  spp33  5.114657e-01
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## 6735  spp398  spp33  5.897396e-01
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## 6737   spp40  spp33  3.977435e-01
## 6738  spp406  spp33  5.858383e-01
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## 6780  spp668  spp33 -9.261337e-02
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## 15981 spp559 spp679  8.152778e+00
## 15982 spp565 spp679  7.010538e-01
## 15983 spp567 spp679  7.010538e-01
## 15984 spp569 spp679  1.153439e+00
## 15985  spp59 spp679  5.997863e-01
## 15986   spp6 spp679  7.010538e-01
## 15987  spp60 spp679  6.223723e-01
## 15988 spp601 spp679  5.216687e-01
## 15989 spp604 spp679  8.594362e-01
## 15990  spp62 spp679  2.389685e-01
## 15991 spp634 spp679 -6.577526e-01
## 15992 spp639 spp679  4.328617e-01
## 15993 spp653 spp679  7.010538e-01
## 15994 spp654 spp679  5.708541e-01
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## 15996 spp668 spp679  7.010538e-01
## 15997 spp679 spp679  1.000000e+00
## 15998 spp684 spp679  9.470460e-01
## 15999  spp85 spp679  4.273457e-01
## 16000   spp9 spp679  5.782357e-01
## 16001 spp101 spp684  8.332113e-01
## 16002 spp103 spp684  9.548197e-02
## 16003 spp104 spp684  1.258427e+00
## 16004 spp110 spp684  3.559431e+00
## 16005 spp114 spp684 -6.800635e-01
## 16006 spp116 spp684  8.972450e-01
## 16007 spp126 spp684  1.272667e+00
## 16008 spp133 spp684 -4.957404e-01
## 16009 spp139 spp684  4.611695e-02
## 16010 spp152 spp684  1.004425e-01
## 16011 spp165 spp684  8.900257e-01
## 16012 spp168 spp684  8.500038e-01
## 16013 spp169 spp684 -1.814549e+00
## 16014 spp177 spp684 -3.514949e-01
## 16015 spp185 spp684  1.081030e+00
## 16016   spp2 spp684 -1.048417e-01
## 16017 spp204 spp684  1.046441e+00
## 16018 spp209 spp684  6.080001e-01
## 16019  spp21 spp684  2.753390e-01
## 16020 spp216 spp684  3.224398e-01
## 16021  spp22 spp684  4.902638e-01
## 16022 spp220 spp684  1.417192e+00
## 16023 spp231 spp684 -1.807590e+00
## 16024 spp232 spp684  8.972450e-01
## 16025 spp238 spp684 -1.271104e-01
## 16026 spp243 spp684 -7.158341e-02
## 16027 spp251 spp684 -4.999218e-01
## 16028 spp252 spp684  1.221967e+00
## 16029 spp253 spp684  7.471512e-01
## 16030 spp256 spp684  1.489663e+00
## 16031 spp257 spp684  2.975103e-01
## 16032 spp259 spp684  7.471512e-01
## 16033 spp267 spp684 -1.360438e-01
## 16034  spp27 spp684  7.471512e-01
## 16035 spp271 spp684  1.025255e+01
## 16036 spp272 spp684  2.230961e+00
## 16037 spp273 spp684 -1.903602e-01
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## 16039 spp285 spp684  5.801135e-01
## 16040 spp286 spp684  9.514223e-01
## 16041 spp290 spp684  7.159382e-01
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## 16043 spp296 spp684  1.972877e+00
## 16044 spp301 spp684  5.187171e-02
## 16045 spp305 spp684  1.197255e+00
## 16046 spp306 spp684  2.460700e-01
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## 16049 spp316 spp684 -1.807590e+00
## 16050 spp319 spp684  3.057296e-01
## 16051  spp32 spp684  1.287696e-01
## 16052 spp329 spp684  4.104314e-01
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## 16054 spp332 spp684  9.778916e-01
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## 16056 spp339 spp684  1.494566e+00
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## 16081  spp40 spp684  1.511213e-01
## 16082 spp406 spp684  8.710106e-01
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## 16098 spp501 spp684  6.063813e-01
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## 16100  spp51 spp684  1.212653e+00
## 16101 spp514 spp684 -1.790834e-01
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## 16103 spp519 spp684 -2.684376e+00
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## 16111 spp567 spp684  1.272667e+00
## 16112 spp569 spp684  6.507023e-01
## 16113  spp59 spp684  8.807669e-01
## 16114   spp6 spp684 -5.694634e-01
## 16115  spp60 spp684  7.121818e-01
## 16116 spp601 spp684  7.154016e-01
## 16117 spp604 spp684  7.300488e-01
## 16118  spp62 spp684 -1.842096e-01
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## 16122 spp654 spp684 -2.350733e-01
## 16123 spp659 spp684 -1.487701e-01
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## 16125 spp679 spp684  9.470460e-01
## 16126 spp684 spp684  1.000000e+00
## 16127  spp85 spp684  6.666724e-01
## 16128   spp9 spp684 -1.279324e-01
## 16129 spp101  spp85  5.133592e-01
## 16130 spp103  spp85  6.829377e-01
## 16131 spp104  spp85 -3.928215e-01
## 16132 spp110  spp85 -2.972313e-01
## 16133 spp114  spp85 -6.768680e-01
## 16134 spp116  spp85  6.095761e-01
## 16135 spp126  spp85  6.095761e-01
## 16136 spp133  spp85 -1.631069e+00
## 16137 spp139  spp85  5.202767e-01
## 16138 spp152  spp85  4.358109e-01
## 16139 spp165  spp85  4.674006e-01
## 16140 spp168  spp85  2.894753e-01
## 16141 spp169  spp85  1.251536e+00
## 16142 spp177  spp85 -3.961347e-01
## 16143 spp185  spp85  1.363623e+00
## 16144   spp2  spp85 -1.198565e+00
## 16145 spp204  spp85  5.154755e-01
## 16146 spp209  spp85  5.133582e-01
## 16147  spp21  spp85 -3.171829e-01
## 16148 spp216  spp85  4.215411e-01
## 16149  spp22  spp85  8.473802e-01
## 16150 spp220  spp85  1.116925e+00
## 16151 spp231  spp85 -1.395194e+01
## 16152 spp232  spp85  6.095761e-01
## 16153 spp238  spp85  6.095761e-01
## 16154 spp243  spp85  2.924216e-01
## 16155 spp251  spp85 -1.879105e+00
## 16156 spp252  spp85  1.427424e+00
## 16157 spp253  spp85  6.095761e-01
## 16158 spp256  spp85  1.613154e+00
## 16159 spp257  spp85  4.685886e-01
## 16160 spp259  spp85  6.095761e-01
## 16161 spp267  spp85 -7.430811e+00
## 16162  spp27  spp85  6.095761e-01
## 16163 spp271  spp85 -2.904712e+01
## 16164 spp272  spp85  2.689225e+00
## 16165 spp273  spp85  6.019783e-02
## 16166 spp279  spp85  6.095761e-01
## 16167 spp285  spp85  4.411415e-01
## 16168 spp286  spp85 -1.192649e-01
## 16169 spp290  spp85  6.204081e-01
## 16170 spp293  spp85  6.095761e-01
## 16171 spp296  spp85  3.350698e+00
## 16172 spp301  spp85  1.786623e+00
## 16173 spp305  spp85  6.095761e-01
## 16174 spp306  spp85  4.886199e-01
## 16175 spp308  spp85  6.095761e-01
## 16176 spp310  spp85  1.444292e+00
## 16177 spp316  spp85 -1.395194e+01
## 16178 spp319  spp85  5.326217e-01
## 16179  spp32  spp85 -9.517943e-01
## 16180 spp329  spp85  5.184265e-01
## 16181  spp33  spp85  3.594912e-01
## 16182 spp332  spp85  6.095761e-01
## 16183 spp337  spp85  3.520582e+00
## 16184 spp339  spp85  6.095761e-01
## 16185 spp340  spp85  1.149713e+00
## 16186 spp344  spp85  3.336843e+01
## 16187 spp349  spp85 -3.928215e-01
## 16188 spp353  spp85 -2.444750e-01
## 16189 spp354  spp85 -7.017216e-01
## 16190  spp36  spp85  3.923277e-01
## 16191 spp362  spp85 -2.691589e-01
## 16192 spp366  spp85 -2.747689e-01
## 16193 spp370  spp85 -3.107623e-01
## 16194 spp373  spp85  6.095761e-01
## 16195 spp375  spp85  6.095761e-01
## 16196 spp380  spp85  6.095761e-01
## 16197 spp381  spp85  5.190648e-01
## 16198 spp384  spp85  7.161314e-01
## 16199 spp386  spp85  1.394137e+00
## 16200 spp387  spp85 -9.805325e-01
## 16201 spp388  spp85 -1.395194e+01
## 16202 spp389  spp85  3.566750e-01
## 16203 spp392  spp85 -1.154700e+00
## 16204 spp393  spp85  5.749010e-01
## 16205 spp394  spp85  4.998650e-01
## 16206 spp395  spp85  6.095761e-01
## 16207 spp398  spp85  6.095761e-01
## 16208   spp4  spp85  6.095761e-01
## 16209  spp40  spp85 -2.049065e-01
## 16210 spp406  spp85  6.055437e-01
## 16211 spp407  spp85 -2.952093e-01
## 16212 spp410  spp85 -1.192649e-01
## 16213 spp416  spp85  5.095909e-01
## 16214 spp418  spp85  2.601028e-01
## 16215 spp421  spp85  3.401859e-01
## 16216 spp439  spp85  5.752594e-01
## 16217 spp457  spp85 -3.928215e-01
## 16218 spp459  spp85 -1.355516e+00
## 16219 spp467  spp85  5.189393e-01
## 16220 spp469  spp85  9.562354e+00
## 16221 spp475  spp85 -1.486274e-01
## 16222 spp481  spp85 -1.028399e+00
## 16223 spp483  spp85  3.559592e-01
## 16224 spp490  spp85  3.829734e-01
## 16225 spp492  spp85  4.523492e-01
## 16226 spp501  spp85 -2.769298e-01
## 16227 spp503  spp85  5.290445e-01
## 16228  spp51  spp85  6.095761e-01
## 16229 spp514  spp85  7.425542e-01
## 16230 spp515  spp85  3.959376e-01
## 16231 spp519  spp85 -2.145911e+00
## 16232 spp521  spp85  2.597242e+00
## 16233 spp527  spp85 -1.204737e-19
## 16234 spp537  spp85  4.877903e-01
## 16235 spp547  spp85  3.475201e-01
## 16236 spp555  spp85  3.625734e+00
## 16237 spp559  spp85 -3.484895e-01
## 16238 spp565  spp85 -1.993134e-01
## 16239 spp567  spp85  6.095761e-01
## 16240 spp569  spp85  5.834581e-01
## 16241  spp59  spp85  5.215226e-01
## 16242   spp6  spp85 -8.892443e-01
## 16243  spp60  spp85 -2.712429e-01
## 16244 spp601  spp85  4.535982e-01
## 16245 spp604  spp85 -3.202962e-01
## 16246  spp62  spp85 -3.100127e-01
## 16247 spp634  spp85  2.583657e-01
## 16248 spp639  spp85 -1.743479e+00
## 16249 spp653  spp85  6.095761e-01
## 16250 spp654  spp85 -1.563609e+00
## 16251 spp659  spp85  6.095761e-01
## 16252 spp668  spp85  6.095761e-01
## 16253 spp679  spp85  4.273457e-01
## 16254 spp684  spp85  6.666724e-01
## 16255  spp85  spp85  1.000000e+00
## 16256   spp9  spp85 -1.248292e+00
## 16257 spp101   spp9  6.946194e-01
## 16258 spp103   spp9  2.552735e+00
## 16259 spp104   spp9  8.248093e-01
## 16260 spp110   spp9  8.248093e-01
## 16261 spp114   spp9  3.476273e-01
## 16262 spp116   spp9  8.614376e-01
## 16263 spp126   spp9  8.248093e-01
## 16264 spp133   spp9  9.717772e-01
## 16265 spp139   spp9  7.039795e-01
## 16266 spp152   spp9  5.896899e-01
## 16267 spp165   spp9  3.516240e-01
## 16268 spp168   spp9  5.221805e-01
## 16269 spp169   spp9  3.098150e-01
## 16270 spp177   spp9 -4.211103e-01
## 16271 spp185   spp9  5.849145e-01
## 16272   spp2   spp9  9.868882e-01
## 16273 spp204   spp9  3.156557e-01
## 16274 spp209   spp9  4.949015e-01
## 16275  spp21   spp9  4.931101e-01
## 16276 spp216   spp9  5.703816e-01
## 16277  spp22   spp9  6.558726e-01
## 16278 spp220   spp9  8.248093e-01
## 16279 spp231   spp9  1.937050e+00
## 16280 spp232   spp9  8.248093e-01
## 16281 spp238   spp9  8.248093e-01
## 16282 spp243   spp9  3.956717e-01
## 16283 spp251   spp9  1.037339e+00
## 16284 spp252   spp9  8.365368e-01
## 16285 spp253   spp9  8.248093e-01
## 16286 spp256   spp9  6.601781e-01
## 16287 spp257   spp9  6.340409e-01
## 16288 spp259   spp9  8.248093e-01
## 16289 spp267   spp9  9.984492e-02
## 16290  spp27   spp9  8.248093e-01
## 16291 spp271   spp9  9.714228e-01
## 16292 spp272   spp9  8.248093e-01
## 16293 spp273   spp9 -8.288093e-02
## 16294 spp279   spp9  8.248093e-01
## 16295 spp285   spp9  5.969026e-01
## 16296 spp286   spp9  8.248093e-01
## 16297 spp290   spp9  1.048414e+00
## 16298 spp293   spp9  8.248093e-01
## 16299 spp296   spp9  2.998671e-01
## 16300 spp301   spp9  5.881047e-01
## 16301 spp305   spp9  4.930905e-01
## 16302 spp306   spp9  6.611450e-01
## 16303 spp308   spp9  8.248093e-01
## 16304 spp310   spp9  7.830152e-01
## 16305 spp316   spp9  1.937050e+00
## 16306 spp319   spp9  7.206834e-01
## 16307  spp32   spp9  9.371799e-01
## 16308 spp329   spp9  3.635226e+00
## 16309  spp33   spp9  4.864227e-01
## 16310 spp332   spp9  8.248093e-01
## 16311 spp337   spp9 -7.115028e-01
## 16312 spp339   spp9  1.977209e-01
## 16313 spp340   spp9 -2.678483e+00
## 16314 spp344   spp9  7.531135e-01
## 16315 spp349   spp9  8.248093e-01
## 16316 spp353   spp9  8.248093e-01
## 16317 spp354   spp9  1.008825e+00
## 16318  spp36   spp9  5.308533e-01
## 16319 spp362   spp9  7.114279e-01
## 16320 spp366   spp9  7.255570e-01
## 16321 spp370   spp9  8.792512e-01
## 16322 spp373   spp9  8.248093e-01
## 16323 spp375   spp9  8.248093e-01
## 16324 spp380   spp9  8.614376e-01
## 16325 spp381   spp9  7.023397e-01
## 16326 spp384   spp9  4.662608e+00
## 16327 spp386   spp9  8.465925e-01
## 16328 spp387   spp9  1.016551e+00
## 16329 spp388   spp9  1.937050e+00
## 16330 spp389   spp9  1.823601e+01
## 16331 spp392   spp9  7.674135e-01
## 16332 spp393   spp9  7.778909e-01
## 16333 spp394   spp9  6.763606e-01
## 16334 spp395   spp9  8.614376e-01
## 16335 spp398   spp9  8.248093e-01
## 16336   spp4   spp9  9.271948e-01
## 16337  spp40   spp9  5.562838e-01
## 16338 spp406   spp9  8.193530e-01
## 16339 spp407   spp9  9.324279e-01
## 16340 spp410   spp9  8.248093e-01
## 16341 spp416   spp9  6.895206e-01
## 16342 spp418   spp9  4.859402e-01
## 16343 spp421   spp9  1.570648e-01
## 16344 spp439   spp9  3.000285e+00
## 16345 spp457   spp9  8.248093e-01
## 16346 spp459   spp9  9.597135e-01
## 16347 spp467   spp9  7.021698e-01
## 16348 spp469   spp9  3.611247e-01
## 16349 spp475   spp9  3.758602e-01
## 16350 spp481   spp9  8.037026e-01
## 16351 spp483   spp9  4.816437e-01
## 16352 spp490   spp9  5.181962e-01
## 16353 spp492   spp9  6.120676e-01
## 16354 spp501   spp9  8.834578e-01
## 16355 spp503   spp9  6.390905e-01
## 16356  spp51   spp9  9.271948e-01
## 16357 spp514   spp9  7.505062e-01
## 16358 spp515   spp9  1.981961e+00
## 16359 spp519   spp9  5.334135e-01
## 16360 spp521   spp9  6.000730e-01
## 16361 spp527   spp9  7.392086e-01
## 16362 spp537   spp9  3.352372e+00
## 16363 spp547   spp9  2.123894e-01
## 16364 spp555   spp9  8.311861e-01
## 16365 spp559   spp9  7.598761e-01
## 16366 spp565   spp9  8.248093e-01
## 16367 spp567   spp9  8.248093e-01
## 16368 spp569   spp9  7.894693e-01
## 16369  spp59   spp9  1.270285e+00
## 16370   spp6   spp9  8.248093e-01
## 16371  spp60   spp9  7.322384e-01
## 16372 spp601   spp9  6.137577e-01
## 16373 spp604   spp9  1.011151e+00
## 16374  spp62   spp9  3.221037e+00
## 16375 spp634   spp9  2.507259e+00
## 16376 spp639   spp9  9.398190e-01
## 16377 spp653   spp9  4.930905e-01
## 16378 spp654   spp9  1.004722e+00
## 16379 spp659   spp9  8.248093e-01
## 16380 spp668   spp9  8.248093e-01
## 16381 spp679   spp9  5.782357e-01
## 16382 spp684   spp9 -1.279324e-01
## 16383  spp85   spp9 -1.248292e+00
## 16384   spp9   spp9  1.000000e+00

Negative values indicate a negative relationship between the relationship among taxa in the reference compared to the treatment. Ideally all relationships should be 1 if the information is perfectly preserved. We can subset the dataset by specific taxa, and use metadata about those taxa to better understand why the relationships change. If we look at taxon 153, we see that it exists in 22 sites. We can look at how the prevalence and abundance of other taxa relate to the predicted relationship between the taxa. First let’s identify low prevalence and high prevalence taxa.

# create values for subsetting
nm<-rownames(model$model$SpeciesMeta)
nm.h<-nm[model$model$SpeciesMeta$prevalence>20]
nm.l<-nm[model$model$SpeciesMeta$prevalence==1]

table(rownames(model$model$SpeciesMeta)==model$QSeq0.5$taxCor.Ratio[model$QSeq0.5$taxCor.Ratio$Var2==nm.l[[1]],1])

## 
## TRUE 
##  128

# plot vs prevalence
plot(model$model$SpeciesMeta$prevalence,model$QSeq0.5$taxCor.Ratio[model$QSeq0.5$taxCor.Ratio$Var2==nm.h[[1]],3], xlab="Prevalence", ylab="taxcor.Ratio")

plot(model$model$SpeciesMeta$mean_abundance,model$QSeq0.5$taxCor.Ratio[model$QSeq0.5$taxCor.Ratio$Var2==nm.h[[1]],3], xlab="mean Abundance", ylab="taxcor.Ratio")

plot(model$model$SpeciesMeta$sd_abundance,model$QSeq0.5$taxCor.Ratio[model$QSeq0.5$taxCor.Ratio$Var2==nm.h[[1]],3], xlab="SD Abundance", ylab="taxcor.Ratio")

We can see in general, the largest errors come from where the prevalence and mean abundance are both low. However, in this example the one difference is a highly prevalent, but low abundance taxon. We can examine how this pattern holds up on a low prevalence taxon.

# check taxa are in the right order
table(rownames(model$model$SpeciesMeta)==model$QSeq0.5$taxCor.Ratio[model$QSeq0.5$taxCor.Ratio$Var2==nm.l[[1]],1])

## 
## TRUE 
##  128

# plot vs prevalence
plot(model$model$SpeciesMeta$prevalence,model$QSeq0.5$taxCor.Ratio[model$QSeq0.5$taxCor.Ratio$Var2==nm.l[[1]],3], xlab="Prevalence", ylab="taxcor.Ratio")

plot(model$model$SpeciesMeta$mean_abundance,model$QSeq0.5$taxCor.Ratio[model$QSeq0.5$taxCor.Ratio$Var2==nm.l[[1]],3], xlab="mean Abundance", ylab="taxcor.Ratio")

plot(model$model$SpeciesMeta$sd_abundance,model$QSeq0.5$taxCor.Ratio[model$QSeq0.5$taxCor.Ratio$Var2==nm.l[[1]],3], xlab="SD Abundance", ylab="taxcor.Ratio")

It is important to note that there are some negative values. The Taxcor is a pearson correlation. The other metrics use a R-sqaured value, which precludes negatives. In this case there is an interpretation: the relationship between taxa is opposite in the reference than in the normalized data. This would be interpreted as potentially a false positive relationship if the relationship is strong enough after normalization.

Model.Microbiome includes several R-ratio metrics for whole community patterns. These are based on the PERMANOVA r-squared value. Model.Microbiome conducts a PERMANOVA of each environmental factor and the categorical factor against a Bray-Curtis transformation of the count table. These are done separately because order of addition of the factors in the model influences the model outcomes; it is easiest to get comparable results run each factor in isolation. For example:

model$raw$PERMANOVA$F1

## 
## Call:
## adonis(formula = x ~ F1, data = y) 
## 
## Permutation: free
## Number of permutations: 999
## 
## Terms added sequentially (first to last)
## 
##           Df SumsOfSqs MeanSqs F.Model      R2 Pr(>F)    
## F1         1    1.0582 1.05818  4.2325 0.13131  0.001 ***
## Residuals 28    7.0003 0.25001         0.86869           
## Total     29    8.0585                 1.00000           
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

The R squared part of the table is taken as a ratio of the reference:

model$raw$PERMANOVA$F1Rratio

##        R ratio Residual ratio          total 
##      0.7448459      1.0546095      1.0000000

We can examine how well each of the environmental and categorical factors are maintained:

model$raw$PERMANOVA$CategoryRratio

##        R ratio Residual ratio          total 
##      0.9748416      1.2468360      1.0000000

model$raw$PERMANOVA$F2Rratio

##        R ratio Residual ratio          total 
##      0.9053624      1.0152625      1.0000000

model$raw$PERMANOVA$F3Rratio

##        R ratio Residual ratio          total 
##      0.6974213      1.1111097      1.0000000

model$raw$PERMANOVA$F4Rratio

##        R ratio Residual ratio          total 
##      0.5404463      1.0310548      1.0000000

model$raw$PERMANOVA$F5Rratio

##        R ratio Residual ratio          total 
##      0.9159684      1.0062026      1.0000000

And of course, we can plot an ordination:

bray_NMDS = ordinate(model$QSeq10$comm, "NMDS", "bray")

## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.1642471 
## Run 1 stress 0.176735 
## Run 2 stress 0.1727819 
## Run 3 stress 0.1735785 
## Run 4 stress 0.1642471 
## ... Procrustes: rmse 1.927883e-05  max resid 9.003283e-05 
## ... Similar to previous best
## Run 5 stress 0.1642471 
## ... Procrustes: rmse 2.898575e-05  max resid 0.0001354968 
## ... Similar to previous best
## Run 6 stress 0.1728475 
## Run 7 stress 0.1745 
## Run 8 stress 0.1642471 
## ... Procrustes: rmse 2.107593e-05  max resid 9.877328e-05 
## ... Similar to previous best
## Run 9 stress 0.173992 
## Run 10 stress 0.1745764 
## Run 11 stress 0.1739759 
## Run 12 stress 0.1735802 
## Run 13 stress 0.1745003 
## Run 14 stress 0.1740196 
## Run 15 stress 0.1642471 
## ... Procrustes: rmse 2.619253e-05  max resid 0.0001229358 
## ... Similar to previous best
## Run 16 stress 0.1816305 
## Run 17 stress 0.1918856 
## Run 18 stress 0.1730667 
## Run 19 stress 0.1739868 
## Run 20 stress 0.1738055 
## *** Solution reached

plot_ordination(model$QSeq10$comm, bray_NMDS, "samples", color="Factor")

We can compare the ordination

bray_NMDS.ref = ordinate(model$model$comm, "NMDS", "bray")

## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.1032647 
## Run 1 stress 0.1352588 
## Run 2 stress 0.1032647 
## ... Procrustes: rmse 2.186653e-06  max resid 5.276753e-06 
## ... Similar to previous best
## Run 3 stress 0.2177992 
## Run 4 stress 0.135307 
## Run 5 stress 0.1032647 
## ... Procrustes: rmse 2.893928e-06  max resid 7.357229e-06 
## ... Similar to previous best
## Run 6 stress 0.1032647 
## ... Procrustes: rmse 5.732468e-06  max resid 1.410858e-05 
## ... Similar to previous best
## Run 7 stress 0.1032647 
## ... New best solution
## ... Procrustes: rmse 1.921246e-06  max resid 3.981697e-06 
## ... Similar to previous best
## Run 8 stress 0.1032647 
## ... Procrustes: rmse 2.514277e-06  max resid 6.607881e-06 
## ... Similar to previous best
## Run 9 stress 0.1032647 
## ... Procrustes: rmse 6.23875e-06  max resid 1.361394e-05 
## ... Similar to previous best
## Run 10 stress 0.1032647 
## ... Procrustes: rmse 2.254725e-06  max resid 8.186324e-06 
## ... Similar to previous best
## Run 11 stress 0.135307 
## Run 12 stress 0.1032647 
## ... Procrustes: rmse 1.557505e-06  max resid 4.857962e-06 
## ... Similar to previous best
## Run 13 stress 0.1032647 
## ... New best solution
## ... Procrustes: rmse 1.408713e-06  max resid 3.149888e-06 
## ... Similar to previous best
## Run 14 stress 0.1032647 
## ... Procrustes: rmse 1.802466e-06  max resid 4.880144e-06 
## ... Similar to previous best
## Run 15 stress 0.1032647 
## ... Procrustes: rmse 8.580318e-07  max resid 2.48826e-06 
## ... Similar to previous best
## Run 16 stress 0.1032647 
## ... Procrustes: rmse 5.220029e-06  max resid 1.34319e-05 
## ... Similar to previous best
## Run 17 stress 0.135307 
## Run 18 stress 0.1032647 
## ... Procrustes: rmse 1.06033e-06  max resid 2.527323e-06 
## ... Similar to previous best
## Run 19 stress 0.3915013 
## Run 20 stress 0.135307 
## *** Solution reached

plot_ordination(model$model$comm, bray_NMDS.ref, "samples", color="Factor")

bray_NMDS.raw = ordinate(model$raw$comm, "NMDS", "bray")

## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.1590721 
## Run 1 stress 0.1594203 
## ... Procrustes: rmse 0.01708649  max resid 0.04928656 
## Run 2 stress 0.15942 
## ... Procrustes: rmse 0.01702016  max resid 0.04931327 
## Run 3 stress 0.1588214 
## ... New best solution
## ... Procrustes: rmse 0.005492935  max resid 0.02168543 
## Run 4 stress 0.1590721 
## ... Procrustes: rmse 0.005474916  max resid 0.02160621 
## Run 5 stress 0.1591219 
## ... Procrustes: rmse 0.01181834  max resid 0.04750845 
## Run 6 stress 0.1588214 
## ... Procrustes: rmse 6.686958e-05  max resid 0.0002144158 
## ... Similar to previous best
## Run 7 stress 0.1777053 
## Run 8 stress 0.1594201 
## Run 9 stress 0.2101728 
## Run 10 stress 0.1776931 
## Run 11 stress 0.1591219 
## ... Procrustes: rmse 0.01180074  max resid 0.047568 
## Run 12 stress 0.1787498 
## Run 13 stress 0.1591231 
## ... Procrustes: rmse 0.01181595  max resid 0.04756514 
## Run 14 stress 0.2089419 
## Run 15 stress 0.1591227 
## ... Procrustes: rmse 0.01188552  max resid 0.04700879 
## Run 16 stress 0.1628561 
## Run 17 stress 0.177478 
## Run 18 stress 0.1588216 
## ... Procrustes: rmse 0.0001685084  max resid 0.0005873744 
## ... Similar to previous best
## Run 19 stress 0.1762812 
## Run 20 stress 0.1588216 
## ... Procrustes: rmse 0.0001306327  max resid 0.0004323713 
## ... Similar to previous best
## *** Solution reached

plot_ordination(model$raw$comm, bray_NMDS.raw, "samples", color="Factor")

bray_NMDS.Q = ordinate(model$QSeq10$comm, "NMDS", "bray")

## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.1642471 
## Run 1 stress 0.1700293 
## Run 2 stress 0.1748909 
## Run 3 stress 0.1748592 
## Run 4 stress 0.1642472 
## ... Procrustes: rmse 6.289248e-05  max resid 0.0002962919 
## ... Similar to previous best
## Run 5 stress 0.169858 
## Run 6 stress 0.1755374 
## Run 7 stress 0.2169519 
## Run 8 stress 0.175577 
## Run 9 stress 0.1732039 
## Run 10 stress 0.1748605 
## Run 11 stress 0.1683357 
## Run 12 stress 0.1738102 
## Run 13 stress 0.1745003 
## Run 14 stress 0.174891 
## Run 15 stress 0.1732877 
## Run 16 stress 0.1642471 
## ... Procrustes: rmse 6.767525e-06  max resid 2.242044e-05 
## ... Similar to previous best
## Run 17 stress 0.1739142 
## Run 18 stress 0.1733601 
## Run 19 stress 0.1642471 
## ... Procrustes: rmse 1.48689e-05  max resid 4.819017e-05 
## ... Similar to previous best
## Run 20 stress 0.1735793 
## *** Solution reached

plot_ordination(model$QSeq10$comm, bray_NMDS.Q, "samples", color="Factor")

While it looks qualitatively like the QSeq ordination might be more accurate to the reference, it’s hard to tell. We can look at the R-Squared Ratio values to figure out which is more accurate. Here’s a spot test:

# raw
model$raw$PERMANOVA$F4Rratio

##        R ratio Residual ratio          total 
##      0.5404463      1.0310548      1.0000000

# QSeq
model$QSeq10$PERMANOVA$F4Rratio

##        R ratio Residual ratio          total 
##      1.0296519      0.9979962      1.0000000

# raw
model$raw$PERMANOVA$CategoryRratio

##        R ratio Residual ratio          total 
##      0.9748416      1.2468360      1.0000000

# QSeq
model$QSeq10$PERMANOVA$CategoryRratio

##        R ratio Residual ratio          total 
##      0.9748584      1.2466705      1.0000000

The category variables look nearly identical, whereas the environmental variables are much better modeled by the QSeq approach. In the next section, we’ll look at how to run multiple simulations to aggregate and statistically evaluate the differences of these approaches within the modeling environment.

Conducting Experiments: Summarizing Outputs

Model.Microbiome has a wrapper that allows the user to iteratively generate random communities with the same experimental conditions. The inputs are the same as before, plus one aditional input to tell the function how many times to iterate. In this case we’ll do 10. We use suppressWarnings because the linear model often produces warnings when it has a perfect fit, and these can clutter the output.

model10<-suppressWarnings(BENCHMARK.MM(reps=10, commonN=30, groupN=20, singleN=5, D=500, V=250, method))

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## rarefying sample Site30

## [1] "metadata complete"
## [1] "QSeq0.5  complete"
## [1] "QSeq1  complete"
## [1] "QSeq2  complete"
## [1] "QSeq3  complete"
## [1] "QSeq10  complete"
## [1] "QSeq100  complete"
## [1] "raw permanova complete"
## [1] "raw LII complete"
## [1] "lmtab raw complete"
## [1] "lmtab model complete"
## [1] "dtab complete"

model10 is now a list object with 10 items, each one as a replicated simulation. This is the basis for us to be able to extract performance metrics and do statistical analyses to compare different normalization methods. Let’s look at some analyses that are possible when we can automate community generation.

We first extract the LII indicator with the function Summarize.LII(), then we melt the dataframe and do a statistical test on it:

model10.LIIsummary<-Summarize.LII(model10, method)
model10.LIIsummary<-melt(model10.LIIsummary, value.name = "Value")

summary(aov(Value~Var2 +Error(Var1/Var2), data=model10.LIIsummary)) # blocks of method are nested within each run

## 
## Error: Var1
##           Df  Sum Sq  Mean Sq F value Pr(>F)
## Residuals  9 0.08029 0.008921               
## 
## Error: Var1:Var2
##           Df  Sum Sq  Mean Sq F value Pr(>F)    
## Var2       5 0.06540 0.013079    55.8 <2e-16 ***
## Residuals 45 0.01055 0.000234                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

TukeyHSD(aov(Value~Var2, data=model10.LIIsummary)) # ignoring the blocks bc TukeyHSD can't handle them. Still tells us which is most significant

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = Value ~ Var2, data = model10.LIIsummary)
## 
## $Var2
##                          diff         lwr          upr     p adj
## QSeq1-QSeq0.5   -0.0501219646 -0.10431368  0.004069752 0.0852237
## QSeq2-QSeq0.5   -0.0822677819 -0.13645950 -0.028076065 0.0005276
## QSeq3-QSeq0.5   -0.0858370714 -0.14002879 -0.031645355 0.0002737
## QSeq10-QSeq0.5  -0.0909402152 -0.14513193 -0.036748499 0.0001049
## QSeq100-QSeq0.5 -0.0915970197 -0.14578874 -0.037405303 0.0000926
## QSeq2-QSeq1     -0.0321458173 -0.08633753  0.022045899 0.5042469
## QSeq3-QSeq1     -0.0357151068 -0.08990682  0.018476610 0.3857092
## QSeq10-QSeq1    -0.0408182506 -0.09500997  0.013373466 0.2433735
## QSeq100-QSeq1   -0.0414750551 -0.09566677  0.012716661 0.2279341
## QSeq3-QSeq2     -0.0035692895 -0.05776101  0.050622427 0.9999591
## QSeq10-QSeq2    -0.0086724333 -0.06286415  0.045519283 0.9969040
## QSeq100-QSeq2   -0.0093292378 -0.06352095  0.044862479 0.9956320
## QSeq10-QSeq3    -0.0051031438 -0.05929486  0.049088573 0.9997616
## QSeq100-QSeq3   -0.0057599483 -0.05995166  0.048431768 0.9995689
## QSeq100-QSeq10  -0.0006568044 -0.05484852  0.053534912 1.0000000

plot(TukeyHSD(aov(Value~Var2, data=model10.LIIsummary))) # visual of confidence intervals

Clearly, the worst performing method is QSeq0.5. This is likely because it effectively leads to undersampling because the detection threshold is so high. Ideally we should choose a threshold value for this method that is sufficiently high enough that all sequences that pass QC in our pipeline are included in the sampling, and not rounded to 0 in any sample.

Let’s look at how all these functionalities can be tied together into a comprehensive test of the strengths (or weaknesses) of a normalization procedure.

We can look at the difference in PERMANOVA outputs:

model10.PCat<-Summarize.PERMANOVA.Rratio(model10, method, "CategoryRratio")

model10.PF1<-Summarize.PERMANOVA.Rratio(model10, method, "F1Rratio")
model10.PF2<-Summarize.PERMANOVA.Rratio(model10, method, "F2Rratio")
model10.PF3<-Summarize.PERMANOVA.Rratio(model10, method, "F3Rratio")
model10.PF4<-Summarize.PERMANOVA.Rratio(model10, method, "F4Rratio")
model10.PF5<-Summarize.PERMANOVA.Rratio(model10, method, "F5Rratio")

model10.PCat

##         QSeq0.5     QSeq1     QSeq2     QSeq3    QSeq10   QSeq100
## rep1  0.9881261 0.9921541 0.9906986 0.9906381 0.9906119 0.9905366
## rep2  0.9884601 0.9878334 0.9886161 0.9883675 0.9883855 0.9883576
## rep3  0.9773214 0.9758738 0.9761179 0.9754467 0.9756708 0.9756950
## rep4  0.9677111 0.9718228 0.9701867 0.9705645 0.9705536 0.9704752
## rep5  0.9786398 0.9744689 0.9835492 0.9837772 0.9830671 0.9832764
## rep6  0.9744107 0.9764489 0.9773352 0.9774028 0.9770839 0.9770245
## rep7  0.9454088 0.9428646 0.9430017 0.9432314 0.9436426 0.9435475
## rep8  0.9877431 0.9839410 0.9849110 0.9846016 0.9847407 0.9846902
## rep9  0.9625179 0.9599453 0.9627013 0.9621837 0.9631343 0.9629951
## rep10 0.9646539 0.9640625 0.9632545 0.9637701 0.9637133 0.9636921

model10.PF1

##         QSeq0.5     QSeq1     QSeq2     QSeq3    QSeq10   QSeq100
## rep1  0.9940840 0.9934145 0.9893918 0.9908630 0.9905719 0.9905493
## rep2  0.9775944 0.9807159 0.9826588 0.9815281 0.9818253 0.9820868
## rep3  0.9607124 0.9648225 0.9617297 0.9606411 0.9614017 0.9618031
## rep4  0.9743669 0.9692017 0.9683153 0.9693053 0.9687634 0.9685723
## rep5  0.9660457 0.9697915 0.9803968 0.9809564 0.9804135 0.9810709
## rep6  0.9778615 0.9745739 0.9744919 0.9742449 0.9746102 0.9746034
## rep7  0.8825335 0.9554767 0.9395778 0.9466839 0.9465838 0.9450085
## rep8  0.9718133 0.9713140 0.9724798 0.9722273 0.9723055 0.9723450
## rep9  0.9865882 0.9768376 0.9829539 0.9808733 0.9828734 0.9826030
## rep10 1.0158277 0.9991268 1.0055697 1.0048206 1.0045588 1.0044677

model10.PF2

##         QSeq0.5     QSeq1     QSeq2     QSeq3    QSeq10   QSeq100
## rep1  0.9799895 0.9812818 0.9817546 0.9819709 0.9815427 0.9816409
## rep2  0.8764698 0.8781803 0.8802367 0.8779104 0.8790458 0.8789169
## rep3  1.0017515 0.9900001 0.9916000 0.9927568 0.9921086 0.9922794
## rep4  0.8995475 0.9058397 0.9012136 0.9031107 0.9024370 0.9029721
## rep5  1.0028392 0.9954152 0.9907016 0.9930782 0.9921611 0.9927491
## rep6  0.9867328 0.9887259 0.9873925 0.9890508 0.9885130 0.9886983
## rep7  0.9001474 0.9013847 0.9027194 0.9004918 0.9007936 0.9011432
## rep8  1.0074141 1.0069980 1.0096261 1.0082990 1.0096237 1.0093167
## rep9  0.8464131 0.8352390 0.8395098 0.8389328 0.8398993 0.8399103
## rep10 0.9497840 0.9494714 0.9493469 0.9483804 0.9492233 0.9493623

model10.PF3

##         QSeq0.5     QSeq1     QSeq2     QSeq3    QSeq10   QSeq100
## rep1  0.9848215 0.9831319 0.9813946 0.9838849 0.9832748 0.9830854
## rep2  0.9761773 0.9753668 0.9766389 0.9759794 0.9760614 0.9759244
## rep3  0.9636922 0.9650680 0.9680485 0.9655182 0.9667143 0.9669182
## rep4  0.9489335 0.9558701 0.9567956 0.9557772 0.9557962 0.9555076
## rep5  0.9830311 0.9798891 0.9857959 0.9855101 0.9839962 0.9840539
## rep6  0.9255259 0.9303482 0.9301719 0.9288404 0.9288173 0.9286932
## rep7  0.9550585 0.9456604 0.9500324 0.9481839 0.9484077 0.9486378
## rep8  1.0009221 1.0004251 1.0019289 0.9990095 1.0004911 1.0005483
## rep9  0.9437705 0.9427215 0.9480851 0.9467291 0.9489354 0.9484727
## rep10 0.9606621 0.9591806 0.9541364 0.9560093 0.9557843 0.9554115

model10.PF4

##         QSeq0.5     QSeq1     QSeq2     QSeq3    QSeq10   QSeq100
## rep1  1.0017923 1.0063945 1.0066836 1.0065263 1.0068951 1.0070115
## rep2  0.9614354 0.9622348 0.9600984 0.9606425 0.9601017 0.9602968
## rep3  0.9129965 0.9162085 0.9215214 0.9185178 0.9224934 0.9230714
## rep4  0.8975698 0.8915768 0.8935027 0.8945583 0.8962629 0.8961651
## rep5  0.9483157 0.9658663 0.9690047 0.9711747 0.9676485 0.9691194
## rep6  0.9400267 0.9295057 0.9291989 0.9291892 0.9299417 0.9301920
## rep7  0.9906456 0.9875782 0.9862913 0.9878382 0.9876615 0.9881708
## rep8  1.0884273 1.1111039 1.1055835 1.1068364 1.1064946 1.1072663
## rep9  0.9531081 0.9452595 0.9573413 0.9549065 0.9579801 0.9579369
## rep10 1.1489594 1.1523233 1.1396955 1.1398546 1.1378130 1.1390252

model10.PF5

##         QSeq0.5     QSeq1     QSeq2     QSeq3    QSeq10   QSeq100
## rep1  0.9797332 0.9814054 0.9803288 0.9831601 0.9822573 0.9827244
## rep2  0.9000598 0.8952694 0.8964603 0.8969274 0.8978841 0.8982260
## rep3  0.9389391 0.9339514 0.9397234 0.9369315 0.9378527 0.9376733
## rep4  0.9785508 0.9757071 0.9753877 0.9763750 0.9762474 0.9762871
## rep5  0.9545484 0.9715013 0.9797089 0.9852004 0.9863477 0.9848842
## rep6  0.9664313 0.9565973 0.9616999 0.9557965 0.9586841 0.9586439
## rep7  0.9622637 0.9602673 0.9607610 0.9610094 0.9609488 0.9611259
## rep8  1.0151497 1.0238623 1.0208628 1.0217522 1.0193835 1.0193256
## rep9  0.9716080 0.9754491 0.9749067 0.9746532 0.9746371 0.9747223
## rep10 0.9220556 0.9218243 0.9255942 0.9239686 0.9228668 0.9231600

NOTE: In general, there are many outputs that a researcher may want to generate and summarize that we have not anticipated. Here are some functions for extracting the R-ratio from the linear models to give a template on the extraction method that works well with the object. This should give a means for researchers to extract and summarize any metric in any way they want. We will use both of these functions later in the analysis.

# get lmRatio ####
Summarize.lmRatiotab.Median<-function(trt, method){
  Ftab<-matrix(NA, nrow = length(trt), ncol = length(method)) # make matrix
  for(i in 1:length(trt)){
    for(j in 1:length(method)){
      Ftab[i,j]<-median(trt[[i]][[method[j]]]$lmRatiotab, na.rm=T)
    #print(sum(trt[[i]][j]$PERMANOVA$aov.tab$F.Model))
  }
}
  rownames(Ftab)<-names(trt)
  colnames(Ftab)<-method
  Ftab
}

Summarize.lmRatiotab.Var<-function(trt, method){
  Ftab<-matrix(NA, nrow = length(trt), ncol = length(method)) # make matrix
  for(i in 1:length(trt)){
    for(j in 1:length(method)){
      Ftab[i,j]<-var(trt[[i]][[method[j]]]$lmRatiotab, na.rm=T)
    #print(sum(trt[[i]][j]$PERMANOVA$aov.tab$F.Model))
  }
}
  rownames(Ftab)<-names(trt)
  colnames(Ftab)<-method
  Ftab
}

The following examples are an actual experiment run to identify biases associated with QSeq protocol, and to optimize QSeq for a number of different interpretive lenses.

Exp. 1: Normalization vs Structure

Let’s say that we want to understand how the effect size of geographic structure within a community interacts with the performance of our normalization technique (or in the case of experimental design, what are the direct assemply effects of the treatment). Model.Microbiome gives us the power to vary the geographic structure/direct effects of the treatment on the community by determining the proportion of each sample that explicitly is determined by the grouping function:

# biogeography begin ####
model10.A<-suppressWarnings(BENCHMARK.MM(reps=10, commonN=53, groupN=1, singleN=1, D=500, V=250, method)) # essentially no filtration by group

model10.B<-suppressWarnings(BENCHMARK.MM(reps=10, commonN=35, groupN=15, singleN=5, D=500, V=250, method)) # ~27% filtration by the group

model10.C<-suppressWarnings(BENCHMARK.MM(reps=10, commonN=20, groupN=20, singleN=15, D=500, V=250, method)) # ~36% filtration by the group

model10.D<-suppressWarnings(BENCHMARK.MM(reps=10, commonN=10, groupN=30, singleN=15, D=500, V=250, method)) # ~55% filtration by the group

First, let’s look at how the structure of the data might interact with our normalization strategy to influence how well information is retained. For this we will extract the LII value. As a reminder, LII correlates each taxon in the normalized dataset against it’s abundance in the reference dataset. The index itself is a sum of 1-R-squared; this means that low LII values mean that overall the R-squared of the taxa against their references were close to 1 (or little information was lost). Conversely, higher values indicate that a lot of information was lost.

# get LII Biogeography ####
method2<- c("raw", method) # add raw data to the methods list to extract it too

# extract the LII from each level of sparcity ####
SummaryLII.model10.A<-as.data.frame(Summarize.LII(model10.A,method2))
SummaryLII.model10.B<-as.data.frame(Summarize.LII(model10.B, method2)) 
SummaryLII.model10.C<-as.data.frame(Summarize.LII(model10.C, method2))
SummaryLII.model10.D<-as.data.frame(Summarize.LII(model10.D, method2))

# prepare data for merging datasets
SummaryLII.model10.A$Level<-c(rep(1,10))
SummaryLII.model10.A<-melt(SummaryLII.model10.A, id.vars = "Level", measure.vars = method2)
SummaryLII.model10.B$Level<-c(rep(2,10))
SummaryLII.model10.B<-melt(SummaryLII.model10.B, id.vars = "Level", measure.vars = method2)
SummaryLII.model10.C$Level<-c(rep(3,10))
SummaryLII.model10.C<-melt(SummaryLII.model10.C, id.vars = "Level", measure.vars = method2)
SummaryLII.model10.D$Level<-c(rep(4,10))
SummaryLII.model10.D<-melt(SummaryLII.model10.D, id.vars = "Level", measure.vars = method2)

# merge datasets
model10Levels<-do.call("rbind", list(SummaryLII.model10.A,SummaryLII.model10.B,SummaryLII.model10.C,SummaryLII.model10.D))

# summarize for plotting
model10Levels.summary2<-data_summary2(model10Levels, varname="value", groupnames=c("Level", "variable"))
model10Levels.summary1<-data_summary(model10Levels, varname="value", groupnames=c("Level", "variable"))
# plot
ggplot(model10Levels.summary2, aes(x=Level, y=value, group = variable, color=variable))+
  geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(.3)) +
  scale_colour_viridis_d(direction=-1)+
  geom_line(position=position_dodge(.3))+
  geom_point(position=position_dodge(.3))+
  xlab("Degree of Structure")+
  ylab("LII Value (Median +/- min/max)")+
  theme_classic()

ggplot(model10Levels.summary1, aes(x=Level, y=value, group = variable, color=variable))+
  geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.3)) +
  scale_colour_viridis_d(direction=-1)+
  geom_line(position=position_dodge(.3))+
  geom_point(position=position_dodge(.3))+
  xlab("Degree of Structure")+
  ylab("LII Value (Mean +/- standard dev)")+
  theme_classic()

Here we can see clearly that the degree of structure in the dataset interacts with the normalization method to affect it’s accuracy. In general, less information is lost in QSeq methods, with the clear distinction being that QSeq0.5 performs worse than non normalizing under certain conditions. We can confirm this with a statistical test:

summary(aov(model10Levels$value~model10Levels$Level*model10Levels$variable))

TukeyHSD(aov(model10Levels$value~model10Levels$Level*model10Levels$variable))

## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## model10Levels$Level

## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## model10Levels$Level, model10Levels$variable

## Warning in TukeyHSD.aov(aov(model10Levels$value ~ model10Levels$Level * :
## 'which' specified some non-factors which will be dropped

Conclusion: we can see clearly that the degree of structure in the dataset interacts with the normalization method to affect how much information is retained on a taxon-by-taxon basis. In all cases the QSeq normalization method out performs un-normalized data at low structure, but at high levels of structure only QSeq2 and QSeq3 parameters continue to consistently outperform the raw variables. Remember that LII reports the degradation of R squared and so is a direct measure of lost information. But it doesn’t provide direct information about how well we can detect environmental drivers for the abundance of taxa.

In this case interpretation is a little more challenging, because we are less interested in the mean value, and more interested in the variance of the values. This is because our metric is a ratio of the R-squared (variance explained) of each taxon by the environment to the same measure of the taxon in the reference dataset. This tells us the relative accuracy with which the normalized dataset is predicting the relationship of each taxon to the environment. Ideally the mean value should be 1 (a perfect fit). But it is possible for the mean to be 1, but the deviation to be substantial if it is balanced in the positive and negative direction. In other words, if the error in the positive and negative direction are equal in size, then even if there is large error in those directions, the mean value will still be 1 (a perfect fit). Thus we might have a perfect fit of the mean, yet have no taxa that is accurately modeled. To account for this, we put larger emphasis on the variance using a levene’s test of equality of variance; but because variances may not be equally balanced in the positive and negative direction we are also still interested in changes in the average value. The two are necessary for accurate interpretation. We find especially for this analysis that outliers unduely affect the mean, so we prefer median for understanding the most common effect

Summarize.lmRatiotab.Var(model10.A, method2)



SM.lmRatio.model10.A<-as.data.frame(Summarize.lmRatiotab.Median(model10.A,method2))
SV.lmRatio.model10.A<-as.data.frame(Summarize.lmRatiotab.Var(model10.A,method2))
SM.lmRatio.model10.B<-as.data.frame(Summarize.lmRatiotab.Median(model10.B,method2))
SV.lmRatio.model10.B<-as.data.frame(Summarize.lmRatiotab.Var(model10.B,method2))
SM.lmRatio.model10.C<-as.data.frame(Summarize.lmRatiotab.Median(model10.C,method2))
SV.lmRatio.model10.C<-as.data.frame(Summarize.lmRatiotab.Var(model10.C,method2))
SM.lmRatio.model10.D<-as.data.frame(Summarize.lmRatiotab.Median(model10.D,method2))
SV.lmRatio.model10.D<-as.data.frame(Summarize.lmRatiotab.Var(model10.D,method2))

# prepare data for merging datasets

SM.lmRatio.model10.A$Level<-c(rep(1,10))
SV.lmRatio.model10.A$Level<-c(rep(1,10))
SM.lmRatio.model10.B$Level<-c(rep(2,10))
SV.lmRatio.model10.B$Level<-c(rep(2,10))
SM.lmRatio.model10.C$Level<-c(rep(3,10))
SV.lmRatio.model10.C$Level<-c(rep(3,10))
SM.lmRatio.model10.D$Level<-c(rep(4,10))
SV.lmRatio.model10.D$Level<-c(rep(4,10))

SM.lmRatio.model10.A<-melt(SM.lmRatio.model10.A, id.vars = "Level", measure.vars = method2)
SV.lmRatio.model10.A<-melt(SV.lmRatio.model10.A, id.vars = "Level", measure.vars = method2)
SM.lmRatio.model10.B<-melt(SM.lmRatio.model10.B, id.vars = "Level", measure.vars = method2)
SV.lmRatio.model10.B<-melt(SV.lmRatio.model10.B, id.vars = "Level", measure.vars = method2)
SM.lmRatio.model10.C<-melt(SM.lmRatio.model10.C, id.vars = "Level", measure.vars = method2)
SV.lmRatio.model10.C<-melt(SV.lmRatio.model10.C, id.vars = "Level", measure.vars = method2)
SM.lmRatio.model10.D<-melt(SM.lmRatio.model10.D, id.vars = "Level", measure.vars = method2)
SV.lmRatio.model10.D<-melt(SV.lmRatio.model10.D, id.vars = "Level", measure.vars = method2)

# merge datasets
SM.lmRatio.model10Levels<-do.call("rbind", list(SM.lmRatio.model10.A,SM.lmRatio.model10.B,SM.lmRatio.model10.C,SM.lmRatio.model10.D))
SV.lmRatio.model10Levels<-do.call("rbind", list(SV.lmRatio.model10.A,SV.lmRatio.model10.B,SV.lmRatio.model10.C,SV.lmRatio.model10.D))


# summarize for plotting
SM.lmRatio.model10.p1<-data_summary(SM.lmRatio.model10Levels, varname="value", groupnames=c("Level", "variable"))
SV.lmRatio.model10.p1<-data_summary(SV.lmRatio.model10Levels, varname="value", groupnames=c("Level", "variable"))
# plot
SM.lmRatio.model10.p2<-data_summary2(SM.lmRatio.model10Levels, varname="value", groupnames=c("Level", "variable"))
SV.lmRatio.model10.p2<-data_summary2(SV.lmRatio.model10Levels, varname="value", groupnames=c("Level", "variable"))
# plot
ggplot(SM.lmRatio.model10.p1, aes(x=Level, y=value, group = variable, color=variable))+
  geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.3)) +
  scale_colour_viridis_d(direction=-1)+
  geom_line(position=position_dodge(.3))+
  geom_point(position=position_dodge(.3))+
  xlab("Degree of Structure")+
  ylab("Mean lmRatio (Mean +/- sd)")+
  theme_classic()

ggplot(SV.lmRatio.model10.p1, aes(x=Level, y=value, group = variable, color=variable))+scale_colour_viridis_d(direction=-1)+
  geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.3)) +
  geom_line(position=position_dodge(.3))+
  geom_point(position=position_dodge(.3))+
  xlab("Degree of Structure")+
  ylab("Variance lmRatio (Mean +/- sd)")+
  theme_classic()

ggplot(SM.lmRatio.model10.p2, aes(x=Level, y=value, group = variable, color=variable))+
  geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(.3)) +
  scale_colour_viridis_d(direction=-1)+
  geom_line(position=position_dodge(.3))+
  geom_point(position=position_dodge(.3))+
  xlab("Degree of Structure")+
  ylab("Median lmRatio (Median +/- min/max)")+
  theme_classic()

ggplot(SV.lmRatio.model10.p2, aes(x=Level, y=log(value), group = variable, color=variable))+scale_colour_viridis_d(direction=-1)+
  geom_errorbar(aes(ymin=log(low), ymax=log(high)), width=.1, position=position_dodge(.3)) +
  geom_line(position=position_dodge(.3))+
  geom_point(position=position_dodge(.3))+
  xlab("Degree of Structure")+
  ylab("log Variance lmRatio (Median +/- min/max)")+
  theme_classic()

… and run statistics to see the effect:

summary(aov(SM.lmRatio.model10Levels$value~SM.lmRatio.model10Levels$Level*SM.lmRatio.model10Levels$variable))

##                                                                   Df Sum Sq
## SM.lmRatio.model10Levels$Level                                     1 1.1915
## SM.lmRatio.model10Levels$variable                                  6 0.0851
## SM.lmRatio.model10Levels$Level:SM.lmRatio.model10Levels$variable   6 0.0728
## Residuals                                                        266 1.3187
##                                                                  Mean Sq
## SM.lmRatio.model10Levels$Level                                    1.1915
## SM.lmRatio.model10Levels$variable                                 0.0142
## SM.lmRatio.model10Levels$Level:SM.lmRatio.model10Levels$variable  0.0121
## Residuals                                                         0.0050
##                                                                  F value Pr(>F)
## SM.lmRatio.model10Levels$Level                                   240.335 <2e-16
## SM.lmRatio.model10Levels$variable                                  2.860 0.0102
## SM.lmRatio.model10Levels$Level:SM.lmRatio.model10Levels$variable   2.448 0.0254
## Residuals                                                                      
##                                                                     
## SM.lmRatio.model10Levels$Level                                   ***
## SM.lmRatio.model10Levels$variable                                *  
## SM.lmRatio.model10Levels$Level:SM.lmRatio.model10Levels$variable *  
## Residuals                                                           
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

TukeyHSD(aov(SM.lmRatio.model10Levels$value~SM.lmRatio.model10Levels$Level*SM.lmRatio.model10Levels$variable))

## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## SM.lmRatio.model10Levels$Level

## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## SM.lmRatio.model10Levels$Level, SM.lmRatio.model10Levels$variable

## Warning in TukeyHSD.aov(aov(SM.lmRatio.model10Levels$value ~
## SM.lmRatio.model10Levels$Level * : 'which' specified some non-factors which will
## be dropped

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = SM.lmRatio.model10Levels$value ~ SM.lmRatio.model10Levels$Level * SM.lmRatio.model10Levels$variable)
## 
## $`SM.lmRatio.model10Levels$variable`
##                          diff          lwr        upr     p adj
## QSeq0.5-raw      1.058848e-02 -0.036188123 0.05736509 0.9939723
## QSeq1-raw        3.613214e-02 -0.010644468 0.08290874 0.2502893
## QSeq2-raw        4.398326e-02 -0.002793347 0.09075987 0.0806766
## QSeq3-raw        4.474180e-02 -0.002034802 0.09151841 0.0711136
## QSeq10-raw       4.454871e-02 -0.002227892 0.09132532 0.0734543
## QSeq100-raw      4.479576e-02 -0.001980850 0.09157236 0.0704707
## QSeq1-QSeq0.5    2.554365e-02 -0.021232951 0.07232026 0.6679591
## QSeq2-QSeq0.5    3.339478e-02 -0.013381830 0.08017138 0.3432942
## QSeq3-QSeq0.5    3.415332e-02 -0.012623285 0.08092993 0.3158560
## QSeq10-QSeq0.5   3.396023e-02 -0.012816375 0.08073684 0.3227258
## QSeq100-QSeq0.5  3.420727e-02 -0.012569333 0.08098388 0.3139508
## QSeq2-QSeq1      7.851122e-03 -0.038925484 0.05462773 0.9988588
## QSeq3-QSeq1      8.609666e-03 -0.038166940 0.05538627 0.9980786
## QSeq10-QSeq1     8.416576e-03 -0.038360030 0.05519318 0.9983087
## QSeq100-QSeq1    8.663618e-03 -0.038112988 0.05544022 0.9980101
## QSeq3-QSeq2      7.585442e-04 -0.046018062 0.04753515 1.0000000
## QSeq10-QSeq2     5.654543e-04 -0.046211152 0.04734206 1.0000000
## QSeq100-QSeq2    8.124963e-04 -0.045964110 0.04758910 1.0000000
## QSeq10-QSeq3    -1.930899e-04 -0.046969696 0.04658352 1.0000000
## QSeq100-QSeq3    5.395206e-05 -0.046722654 0.04683056 1.0000000
## QSeq100-QSeq10   2.470420e-04 -0.046529564 0.04702365 1.0000000

summary(aov(SV.lmRatio.model10Levels$value~SV.lmRatio.model10Levels$Level*SV.lmRatio.model10Levels$variable))

##                                                                   Df Sum Sq
## SV.lmRatio.model10Levels$Level                                     1 0.1173
## SV.lmRatio.model10Levels$variable                                  6 0.1450
## SV.lmRatio.model10Levels$Level:SV.lmRatio.model10Levels$variable   6 0.0072
## Residuals                                                        266 0.8183
##                                                                  Mean Sq
## SV.lmRatio.model10Levels$Level                                   0.11726
## SV.lmRatio.model10Levels$variable                                0.02416
## SV.lmRatio.model10Levels$Level:SV.lmRatio.model10Levels$variable 0.00120
## Residuals                                                        0.00308
##                                                                  F value
## SV.lmRatio.model10Levels$Level                                    38.117
## SV.lmRatio.model10Levels$variable                                  7.853
## SV.lmRatio.model10Levels$Level:SV.lmRatio.model10Levels$variable   0.389
## Residuals                                                               
##                                                                    Pr(>F)    
## SV.lmRatio.model10Levels$Level                                   2.48e-09 ***
## SV.lmRatio.model10Levels$variable                                8.46e-08 ***
## SV.lmRatio.model10Levels$Level:SV.lmRatio.model10Levels$variable    0.886    
## Residuals                                                                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

TukeyHSD(aov(SV.lmRatio.model10Levels$value~SV.lmRatio.model10Levels$Level*SV.lmRatio.model10Levels$variable))

## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## SV.lmRatio.model10Levels$Level

## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## SV.lmRatio.model10Levels$Level, SV.lmRatio.model10Levels$variable

## Warning in TukeyHSD.aov(aov(SV.lmRatio.model10Levels$value ~
## SV.lmRatio.model10Levels$Level * : 'which' specified some non-factors which will
## be dropped

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = SV.lmRatio.model10Levels$value ~ SV.lmRatio.model10Levels$Level * SV.lmRatio.model10Levels$variable)
## 
## $`SV.lmRatio.model10Levels$variable`
##                          diff          lwr          upr     p adj
## QSeq0.5-raw      0.0430083257  0.006160901  0.079855750 0.0108173
## QSeq1-raw        0.0008151688 -0.036032255  0.037662593 1.0000000
## QSeq2-raw       -0.0219323982 -0.058779822  0.014915026 0.5705761
## QSeq3-raw       -0.0192015612 -0.056048986  0.017645863 0.7152416
## QSeq10-raw      -0.0248086389 -0.061656063  0.012038785 0.4168778
## QSeq100-raw     -0.0250136742 -0.061861098  0.011833750 0.4064418
## QSeq1-QSeq0.5   -0.0421931569 -0.079040581 -0.005345733 0.0134514
## QSeq2-QSeq0.5   -0.0649407239 -0.101788148 -0.028093300 0.0000069
## QSeq3-QSeq0.5   -0.0622098869 -0.099057311 -0.025362463 0.0000198
## QSeq10-QSeq0.5  -0.0678169646 -0.104664389 -0.030969540 0.0000022
## QSeq100-QSeq0.5 -0.0680219999 -0.104869424 -0.031174576 0.0000020
## QSeq2-QSeq1     -0.0227475670 -0.059594991  0.014099857 0.5261768
## QSeq3-QSeq1     -0.0200167300 -0.056864154  0.016830694 0.6734489
## QSeq10-QSeq1    -0.0256238077 -0.062471232  0.011223617 0.3760302
## QSeq100-QSeq1   -0.0258288430 -0.062676267  0.011018581 0.3660443
## QSeq3-QSeq2      0.0027308369 -0.034116587  0.039578261 0.9999904
## QSeq10-QSeq2    -0.0028762408 -0.039723665  0.033971184 0.9999869
## QSeq100-QSeq2   -0.0030812760 -0.039928700  0.033766148 0.9999803
## QSeq10-QSeq3    -0.0056070777 -0.042454502  0.031240347 0.9993478
## QSeq100-QSeq3   -0.0058121130 -0.042659537  0.031035311 0.9991989
## QSeq100-QSeq10  -0.0002050353 -0.037052460  0.036642389 1.0000000

Conclusion: there is an interaction between the normalization method and the internal structure of the community on our ability to accurately describe the relationship between taxa and the environmental gradients. According to this analysis we should prefer QSeq3,10 and 100.

What about our ability to detect the experimental design? Following the same methodology:

Summarize.lmRatiotabModel.Median<-function(trt, method){
  Ftab<-matrix(NA, nrow = length(trt), ncol = length(method)) # make matrix
  for(i in 1:length(trt)){
    for(j in 1:length(method)){
      Ftab[i,j]<-median(trt[[i]][[method[j]]]$lmRatiotab.model, na.rm=T)
    #print(sum(trt[[i]][j]$PERMANOVA$aov.tab$F.Model))
  }
}
  rownames(Ftab)<-names(trt)
  colnames(Ftab)<-method
  Ftab
}

Summarize.lmRatiotabModel.Var<-function(trt, method){
  Ftab<-matrix(NA, nrow = length(trt), ncol = length(method)) # make matrix
  for(i in 1:length(trt)){
    for(j in 1:length(method)){
      Ftab[i,j]<-var(trt[[i]][[method[j]]]$lmRatiotab.model, na.rm=T)
    #print(sum(trt[[i]][j]$PERMANOVA$aov.tab$F.Model))
  }
}
  rownames(Ftab)<-names(trt)
  colnames(Ftab)<-method
  Ftab
}


SM.lmRatioM.model10.A<-as.data.frame(Summarize.lmRatiotabModel.Median(model10.A,method2))
SV.lmRatioM.model10.A<-as.data.frame(Summarize.lmRatiotabModel.Var(model10.A,method2))
SM.lmRatioM.model10.B<-as.data.frame(Summarize.lmRatiotabModel.Median(model10.B,method2))
SV.lmRatioM.model10.B<-as.data.frame(Summarize.lmRatiotabModel.Var(model10.B,method2))
SM.lmRatioM.model10.C<-as.data.frame(Summarize.lmRatiotabModel.Median(model10.C,method2))
SV.lmRatioM.model10.C<-as.data.frame(Summarize.lmRatiotabModel.Var(model10.C,method2))
SM.lmRatioM.model10.D<-as.data.frame(Summarize.lmRatiotabModel.Median(model10.D,method2))
SV.lmRatioM.model10.D<-as.data.frame(Summarize.lmRatiotabModel.Var(model10.D,method2))

# prepare data for merging datasets

SM.lmRatioM.model10.A$Level<-c(rep(1,10))
SV.lmRatioM.model10.A$Level<-c(rep(1,10))
SM.lmRatioM.model10.B$Level<-c(rep(2,10))
SV.lmRatioM.model10.B$Level<-c(rep(2,10))
SM.lmRatioM.model10.C$Level<-c(rep(3,10))
SV.lmRatioM.model10.C$Level<-c(rep(3,10))
SM.lmRatioM.model10.D$Level<-c(rep(4,10))
SV.lmRatioM.model10.D$Level<-c(rep(4,10))

SM.lmRatioM.model10.A<-melt(SM.lmRatioM.model10.A, id.vars = "Level", measure.vars = method2)
SV.lmRatioM.model10.A<-melt(SV.lmRatioM.model10.A, id.vars = "Level", measure.vars = method2)
SM.lmRatioM.model10.B<-melt(SM.lmRatioM.model10.B, id.vars = "Level", measure.vars = method2)
SV.lmRatioM.model10.B<-melt(SV.lmRatioM.model10.B, id.vars = "Level", measure.vars = method2)
SM.lmRatioM.model10.C<-melt(SM.lmRatioM.model10.C, id.vars = "Level", measure.vars = method2)
SV.lmRatioM.model10.C<-melt(SV.lmRatioM.model10.C, id.vars = "Level", measure.vars = method2)
SM.lmRatioM.model10.D<-melt(SM.lmRatioM.model10.D, id.vars = "Level", measure.vars = method)
SV.lmRatioM.model10.D<-melt(SV.lmRatioM.model10.D, id.vars = "Level", measure.vars = method2)

# merge datasets
SM.lmRatioM.model10Levels<-do.call("rbind", list(SM.lmRatioM.model10.A,SM.lmRatioM.model10.B,SM.lmRatioM.model10.C,SM.lmRatioM.model10.D))
SV.lmRatioM.model10Levels<-do.call("rbind", list(SV.lmRatioM.model10.A,SV.lmRatioM.model10.B,SV.lmRatioM.model10.C,SV.lmRatioM.model10.D))


# summarize for plotting

SM.lmRatioM.model10.p1<-data_summary(SM.lmRatioM.model10Levels, varname="value", groupnames=c("Level", "variable"))
SV.lmRatioM.model10.p1<-data_summary(SV.lmRatioM.model10Levels, varname="value", groupnames=c("Level", "variable"))
SM.lmRatioM.model10.p2<-data_summary2(SM.lmRatioM.model10Levels, varname="value", groupnames=c("Level", "variable"))
SV.lmRatioM.model10.p2<-data_summary2(SV.lmRatioM.model10Levels, varname="value", groupnames=c("Level", "variable"))
# plot
ggplot(SM.lmRatioM.model10.p1, aes(x=Level, y=value, group = variable, color=variable))+
  geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.3)) +
  scale_colour_viridis_d()+
  geom_line(position=position_dodge(.3))+
  geom_point(position=position_dodge(.3))+
  xlab("Degree of Structure")+
  ylab("Median lmRatio.model (Mean +/- sd)")+
  theme_classic()

ggplot(SV.lmRatioM.model10.p1, aes(x=Level, y=value, group = variable, color=variable))+
  geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.3)) +
  scale_colour_viridis_d(direction=-1)+
  geom_line(position=position_dodge(.3))+
  geom_point(position=position_dodge(.3))+
  xlab("Degree of Structure")+
  ylab("Variance lmRatio.model (Mean +/- sd)")+
  
  theme_classic()

ggplot(SM.lmRatioM.model10.p2, aes(x=Level, y=value, group = variable, color=variable))+
  geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(.3)) +
  scale_colour_viridis_d()+
  geom_line(position=position_dodge(.3))+
  geom_point(position=position_dodge(.3))+
  xlab("Degree of Structure")+
  ylab("Median lmRatio.model (Median +/- min/max)")+
  theme_classic()

ggplot(SV.lmRatioM.model10.p2, aes(x=Level, y=log(value), group = variable, color=variable))+
  geom_errorbar(aes(ymin=log(low), ymax=log(high)), width=.1, position=position_dodge(.3)) +
  scale_colour_viridis_d(direction=-1)+
  geom_line(position=position_dodge(.3))+
  geom_point(position=position_dodge(.3))+
  xlab("Degree of Structure")+
  ylab("Variance lmRatio.model (Median +/- min/max)")+
  
  theme_classic()

And again we do the stats:

summary(aov(SM.lmRatioM.model10Levels$value~SM.lmRatioM.model10Levels$Level*SM.lmRatioM.model10Levels$variable))

##                                                                     Df Sum Sq
## SM.lmRatioM.model10Levels$Level                                      1 0.8811
## SM.lmRatioM.model10Levels$variable                                   6 0.0465
## SM.lmRatioM.model10Levels$Level:SM.lmRatioM.model10Levels$variable   6 0.0472
## Residuals                                                          256 1.2936
##                                                                    Mean Sq
## SM.lmRatioM.model10Levels$Level                                     0.8811
## SM.lmRatioM.model10Levels$variable                                  0.0078
## SM.lmRatioM.model10Levels$Level:SM.lmRatioM.model10Levels$variable  0.0079
## Residuals                                                           0.0051
##                                                                    F value
## SM.lmRatioM.model10Levels$Level                                    174.365
## SM.lmRatioM.model10Levels$variable                                   1.534
## SM.lmRatioM.model10Levels$Level:SM.lmRatioM.model10Levels$variable   1.556
## Residuals                                                                 
##                                                                    Pr(>F)    
## SM.lmRatioM.model10Levels$Level                                    <2e-16 ***
## SM.lmRatioM.model10Levels$variable                                  0.167    
## SM.lmRatioM.model10Levels$Level:SM.lmRatioM.model10Levels$variable  0.161    
## Residuals                                                                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

TukeyHSD(aov(SM.lmRatioM.model10Levels$value~SM.lmRatioM.model10Levels$variable)) # something wrong here?

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = SM.lmRatioM.model10Levels$value ~ SM.lmRatioM.model10Levels$variable)
## 
## $`SM.lmRatioM.model10Levels$variable`
##                          diff         lwr        upr     p adj
## QSeq0.5-raw     -0.0056695427 -0.07139375 0.06005466 0.9999763
## QSeq1-raw        0.0230401489 -0.04268406 0.08876435 0.9438091
## QSeq2-raw        0.0323009994 -0.03342321 0.09802521 0.7679967
## QSeq3-raw        0.0316789184 -0.03404529 0.09740312 0.7839327
## QSeq10-raw       0.0330173453 -0.03270686 0.09874155 0.7490568
## QSeq100-raw      0.0325037550 -0.03322045 0.09822796 0.7626979
## QSeq1-QSeq0.5    0.0287096916 -0.03213910 0.08955848 0.8004986
## QSeq2-QSeq0.5    0.0379705421 -0.02287825 0.09881933 0.5127573
## QSeq3-QSeq0.5    0.0373484612 -0.02350033 0.09819725 0.5332020
## QSeq10-QSeq0.5   0.0386868880 -0.02216190 0.09953568 0.4893693
## QSeq100-QSeq0.5  0.0381732977 -0.02267549 0.09902209 0.5061178
## QSeq2-QSeq1      0.0092608505 -0.05158794 0.07010964 0.9993468
## QSeq3-QSeq1      0.0086387695 -0.05221002 0.06948756 0.9995621
## QSeq10-QSeq1     0.0099771964 -0.05087159 0.07082599 0.9990000
## QSeq100-QSeq1    0.0094636061 -0.05138518 0.07031240 0.9992605
## QSeq3-QSeq2     -0.0006220810 -0.06147087 0.06022671 1.0000000
## QSeq10-QSeq2     0.0007163459 -0.06013245 0.06156514 1.0000000
## QSeq100-QSeq2    0.0002027556 -0.06064604 0.06105155 1.0000000
## QSeq10-QSeq3     0.0013384269 -0.05951036 0.06218722 1.0000000
## QSeq100-QSeq3    0.0008248366 -0.06002395 0.06167363 1.0000000
## QSeq100-QSeq10  -0.0005135903 -0.06136238 0.06033520 1.0000000

summary(aov(SV.lmRatioM.model10Levels$value~SV.lmRatioM.model10Levels$Level*SV.lmRatioM.model10Levels$variable))

##                                                                     Df Sum Sq
## SV.lmRatioM.model10Levels$Level                                      1 0.0564
## SV.lmRatioM.model10Levels$variable                                   6 0.7198
## SV.lmRatioM.model10Levels$Level:SV.lmRatioM.model10Levels$variable   6 0.2731
## Residuals                                                          266 2.5158
##                                                                    Mean Sq
## SV.lmRatioM.model10Levels$Level                                    0.05645
## SV.lmRatioM.model10Levels$variable                                 0.11997
## SV.lmRatioM.model10Levels$Level:SV.lmRatioM.model10Levels$variable 0.04551
## Residuals                                                          0.00946
##                                                                    F value
## SV.lmRatioM.model10Levels$Level                                      5.968
## SV.lmRatioM.model10Levels$variable                                  12.685
## SV.lmRatioM.model10Levels$Level:SV.lmRatioM.model10Levels$variable   4.812
## Residuals                                                                 
##                                                                      Pr(>F)    
## SV.lmRatioM.model10Levels$Level                                    0.015217 *  
## SV.lmRatioM.model10Levels$variable                                 1.38e-12 ***
## SV.lmRatioM.model10Levels$Level:SV.lmRatioM.model10Levels$variable 0.000111 ***
## Residuals                                                                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

TukeyHSD(aov(SV.lmRatioM.model10Levels$value~SV.lmRatioM.model10Levels$Level*SV.lmRatioM.model10Levels$variable))

## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## SV.lmRatioM.model10Levels$Level

## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## SV.lmRatioM.model10Levels$Level, SV.lmRatioM.model10Levels$variable

## Warning in TukeyHSD.aov(aov(SV.lmRatioM.model10Levels$value ~
## SV.lmRatioM.model10Levels$Level * : 'which' specified some non-factors which
## will be dropped

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = SV.lmRatioM.model10Levels$value ~ SV.lmRatioM.model10Levels$Level * SV.lmRatioM.model10Levels$variable)
## 
## $`SV.lmRatioM.model10Levels$variable`
##                          diff         lwr          upr     p adj
## QSeq0.5-raw     -0.0632370521 -0.12784662  0.001372512 0.0595331
## QSeq1-raw       -0.1113114603 -0.17592102 -0.046701896 0.0000122
## QSeq2-raw       -0.1338000916 -0.19840966 -0.069190527 0.0000001
## QSeq3-raw       -0.1392924063 -0.20390197 -0.074682842 0.0000000
## QSeq10-raw      -0.1447583441 -0.20936791 -0.080148780 0.0000000
## QSeq100-raw     -0.1450190766 -0.20962864 -0.080409512 0.0000000
## QSeq1-QSeq0.5   -0.0480744082 -0.11268397  0.016535156 0.2932610
## QSeq2-QSeq0.5   -0.0705630395 -0.13517260 -0.005953475 0.0222406
## QSeq3-QSeq0.5   -0.0760553542 -0.14066492 -0.011445790 0.0097927
## QSeq10-QSeq0.5  -0.0815212920 -0.14613086 -0.016911728 0.0040553
## QSeq100-QSeq0.5 -0.0817820245 -0.14639159 -0.017172460 0.0038822
## QSeq2-QSeq1     -0.0224886313 -0.08709820  0.042120933 0.9456854
## QSeq3-QSeq1     -0.0279809460 -0.09259051  0.036628618 0.8576276
## QSeq10-QSeq1    -0.0334468838 -0.09805645  0.031162680 0.7215635
## QSeq100-QSeq1   -0.0337076163 -0.09831718  0.030901948 0.7141271
## QSeq3-QSeq2     -0.0054923147 -0.07010188  0.059117249 0.9999783
## QSeq10-QSeq2    -0.0109582525 -0.07556782  0.053651312 0.9987890
## QSeq100-QSeq2   -0.0112189850 -0.07582855  0.053390579 0.9986164
## QSeq10-QSeq3    -0.0054659378 -0.07007550  0.059143626 0.9999789
## QSeq100-QSeq3   -0.0057266703 -0.07033623  0.058882894 0.9999722
## QSeq100-QSeq10  -0.0002607325 -0.06487030  0.064348832 1.0000000

An emerging pattern that we see here is that raw data without any processing generally performs worst when there is less structure and environmental variables can act more as a filter. Also, in our normalization method QSeq, higher sampling variables that don’t omit low abundance taxa perform better. Higher abundance will continue to perform even better.

Let’s check the accuracy of the model:

# outputs an object with both variance and median
TaxRatio.model10.A<-getTaxCor.Tab(model10.A,method2)
TaxRatio.model10.B<-getTaxCor.Tab(model10.B,method2)
TaxRatio.model10.C<-getTaxCor.Tab(model10.C,method2)
TaxRatio.model10.D<-getTaxCor.Tab(model10.D,method2)

#separate median and variance tables, and melt
V.TaxRatio.model10.A<-melt(TaxRatio.model10.A$V.tax)
M.TaxRatio.model10.A<-melt(TaxRatio.model10.A$Median.tax)
V.TaxRatio.model10.B<-melt(TaxRatio.model10.B$V.tax)
M.TaxRatio.model10.B<-melt(TaxRatio.model10.B$Median.tax)
V.TaxRatio.model10.C<-melt(TaxRatio.model10.C$V.tax)
M.TaxRatio.model10.C<-melt(TaxRatio.model10.C$Median.tax)
V.TaxRatio.model10.D<-melt(TaxRatio.model10.D$V.tax)
M.TaxRatio.model10.D<-melt(TaxRatio.model10.D$Median.tax)

# prepare data for merging datasets
V.TaxRatio.model10.A<-as.data.frame(V.TaxRatio.model10.A)
M.TaxRatio.model10.A<-as.data.frame(M.TaxRatio.model10.A)
V.TaxRatio.model10.B<-as.data.frame(V.TaxRatio.model10.B)
M.TaxRatio.model10.B<-as.data.frame(M.TaxRatio.model10.B)
V.TaxRatio.model10.C<-as.data.frame(V.TaxRatio.model10.C)
M.TaxRatio.model10.C<-as.data.frame(M.TaxRatio.model10.C)
V.TaxRatio.model10.D<-as.data.frame(V.TaxRatio.model10.D)
M.TaxRatio.model10.D<-as.data.frame(M.TaxRatio.model10.D)

V.TaxRatio.model10.A$Level<-c(rep(1,nrow(V.TaxRatio.model10.A)))
V.TaxRatio.model10.B$Level<-c(rep(2,nrow(V.TaxRatio.model10.B)))
V.TaxRatio.model10.C$Level<-c(rep(3,nrow(V.TaxRatio.model10.C)))
V.TaxRatio.model10.D$Level<-c(rep(4,nrow(V.TaxRatio.model10.D)))
M.TaxRatio.model10.A$Level<-c(rep(1,nrow(M.TaxRatio.model10.A)))
M.TaxRatio.model10.B$Level<-c(rep(2,nrow(M.TaxRatio.model10.B)))
M.TaxRatio.model10.C$Level<-c(rep(3,nrow(M.TaxRatio.model10.C)))
M.TaxRatio.model10.D$Level<-c(rep(4,nrow(M.TaxRatio.model10.D)))



# merge datasets
V.TaxRatio.model10Levels<-do.call("rbind", list(V.TaxRatio.model10.A,V.TaxRatio.model10.B,V.TaxRatio.model10.C,V.TaxRatio.model10.D))
M.TaxRatio.model10Levels<-do.call("rbind", list(M.TaxRatio.model10.A,M.TaxRatio.model10.B,M.TaxRatio.model10.C,M.TaxRatio.model10.D))


# summarize for plotting
V.TaxRatio.model10.p1<-data_summary(V.TaxRatio.model10Levels, varname="value", groupnames=c("Level", "Var2"))
M.TaxRatio.model10.p1<-data_summary(M.TaxRatio.model10Levels, varname="value", groupnames=c("Level", "Var2"))
V.TaxRatio.model10.p2<-data_summary2(V.TaxRatio.model10Levels, varname="value", groupnames=c("Level", "Var2"))
M.TaxRatio.model10.p2<-data_summary2(M.TaxRatio.model10Levels, varname="value", groupnames=c("Level", "Var2"))
# plot
ggplot(V.TaxRatio.model10.p1, aes(x=Level, y=value, group = Var2, color=Var2))+
  geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.3)) +
  scale_color_viridis_d(direction=-1)+
  geom_line(position=position_dodge(.3))+
  geom_point(position=position_dodge(.3))+
  xlab("Degree of Structure")+
  ylab("Variance taxRatio (Mean +/- sd)")+
  theme_classic()

ggplot(M.TaxRatio.model10.p1, aes(x=Level, y=value, group = Var2, color=Var2))+
  geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.3)) +
  scale_color_viridis_d(direction=-1)+
  geom_line(position=position_dodge(.3))+
  geom_point(position=position_dodge(.3))+
  xlab("Degree of Structure")+
  ylab("Mean taxRatio (Mean +/- sd)")+
  theme_classic()

ggplot(V.TaxRatio.model10.p2, aes(x=Level, y=log10(value), group = Var2, color=Var2))+
  geom_errorbar(aes(ymin=log10(low), ymax=log10(high)), width=.1, position=position_dodge(.3)) +
  scale_color_viridis_d(direction=-1)+
  geom_line(position=position_dodge(.3))+
  geom_point(position=position_dodge(.3))+
  xlab("Degree of Structure")+
  ylab("Variance taxRatio (Median +/- min/max)")+
  theme_classic()

ggplot(M.TaxRatio.model10.p2, aes(x=Level, y=value, group = Var2, color=Var2))+
  geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(.3)) +
  scale_color_viridis_d(direction=-1)+
  geom_line(position=position_dodge(.3))+
  geom_point(position=position_dodge(.3))+
  xlab("Degree of Structure")+
  ylab("log Median taxRatio (Median +/- min/max)")+
  theme_classic()

Note: In general, the results of this portion of the simulation show that QSeq0.5 underperforms compared to all other QSeq methods; that QSeq methods generally are better at estimating the mean value than un-normalized (have less systemic under or over estimation), but that often at lower degrees of structure the un-normalized dataset has less variance around the mean. But, this portion of the simulation tends to be less stable, and occasionally fails to produce a significant result. Therefore I will give guidelines on how to interpret the outputs, but not discuss specific conclusions.

Generally variance should approach zero, and the mean should approach 1. The greater the deviation of the variance from zero (and the greater the range in variance values), the less accuracy on a taxon-by-taxon basis in estimating relationships among taxa. The farther the mean deviates from 1, the greater the systemic bias (over or underestimation) of the strength of the relationship. Let’s check the stats:

summary(aov(M.TaxRatio.model10Levels$value~M.TaxRatio.model10Levels$Level*M.TaxRatio.model10Levels$Var2))

##                                                               Df Sum Sq Mean Sq
## M.TaxRatio.model10Levels$Level                                 1   74.3   74.31
## M.TaxRatio.model10Levels$Var2                                  6    2.6    0.43
## M.TaxRatio.model10Levels$Level:M.TaxRatio.model10Levels$Var2   6   14.4    2.40
## Residuals                                                    266  530.9    2.00
##                                                              F value   Pr(>F)
## M.TaxRatio.model10Levels$Level                                37.234 3.69e-09
## M.TaxRatio.model10Levels$Var2                                  0.215    0.972
## M.TaxRatio.model10Levels$Level:M.TaxRatio.model10Levels$Var2   1.200    0.306
## Residuals                                                                    
##                                                                 
## M.TaxRatio.model10Levels$Level                               ***
## M.TaxRatio.model10Levels$Var2                                   
## M.TaxRatio.model10Levels$Level:M.TaxRatio.model10Levels$Var2    
## Residuals                                                       
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

TukeyHSD(aov(M.TaxRatio.model10Levels$value~M.TaxRatio.model10Levels$Var2))

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = M.TaxRatio.model10Levels$value ~ M.TaxRatio.model10Levels$Var2)
## 
## $`M.TaxRatio.model10Levels$Var2`
##                         diff        lwr       upr     p adj
## QSeq0.5-raw      0.187238522 -0.8133721 1.1878491 0.9978954
## QSeq1-raw       -0.114817833 -1.1154285 0.8857928 0.9998732
## QSeq2-raw       -0.083411588 -1.0840222 0.9171990 0.9999807
## QSeq3-raw       -0.084835496 -1.0854461 0.9157751 0.9999787
## QSeq10-raw      -0.068804869 -1.0694155 0.9318058 0.9999938
## QSeq100-raw     -0.071544944 -1.0721556 0.9290657 0.9999922
## QSeq1-QSeq0.5   -0.302056355 -1.3026670 0.6985543 0.9728482
## QSeq2-QSeq0.5   -0.270650110 -1.2712607 0.7299605 0.9844919
## QSeq3-QSeq0.5   -0.272074018 -1.2726846 0.7285366 0.9840640
## QSeq10-QSeq0.5  -0.256043391 -1.2566540 0.7445672 0.9883996
## QSeq100-QSeq0.5 -0.258783465 -1.2593941 0.7418272 0.9877309
## QSeq2-QSeq1      0.031406245 -0.9692044 1.0320169 0.9999999
## QSeq3-QSeq1      0.029982337 -0.9706283 1.0305930 1.0000000
## QSeq10-QSeq1     0.046012965 -0.9545977 1.0466236 0.9999994
## QSeq100-QSeq1    0.043272890 -0.9573377 1.0438835 0.9999996
## QSeq3-QSeq2     -0.001423908 -1.0020345 0.9991867 1.0000000
## QSeq10-QSeq2     0.014606720 -0.9860039 1.0152173 1.0000000
## QSeq100-QSeq2    0.011866645 -0.9887440 1.0124773 1.0000000
## QSeq10-QSeq3     0.016030627 -0.9845800 1.0166413 1.0000000
## QSeq100-QSeq3    0.013290552 -0.9873201 1.0139012 1.0000000
## QSeq100-QSeq10  -0.002740075 -1.0033507 0.9978705 1.0000000

summary(aov(V.TaxRatio.model10Levels$value~V.TaxRatio.model10Levels$Level*V.TaxRatio.model10Levels$Var2))

##                                                               Df    Sum Sq
## V.TaxRatio.model10Levels$Level                                 1 7.312e+09
## V.TaxRatio.model10Levels$Var2                                  6 8.470e+08
## V.TaxRatio.model10Levels$Level:V.TaxRatio.model10Levels$Var2   6 1.061e+09
## Residuals                                                    266 1.179e+11
##                                                                Mean Sq F value
## V.TaxRatio.model10Levels$Level                               7.312e+09  16.495
## V.TaxRatio.model10Levels$Var2                                1.412e+08   0.318
## V.TaxRatio.model10Levels$Level:V.TaxRatio.model10Levels$Var2 1.768e+08   0.399
## Residuals                                                    4.433e+08        
##                                                                Pr(>F)    
## V.TaxRatio.model10Levels$Level                               6.42e-05 ***
## V.TaxRatio.model10Levels$Var2                                   0.927    
## V.TaxRatio.model10Levels$Level:V.TaxRatio.model10Levels$Var2    0.879    
## Residuals                                                                
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

TukeyHSD(aov(V.TaxRatio.model10Levels$value~V.TaxRatio.model10Levels$Level*V.TaxRatio.model10Levels$Var2))

## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## V.TaxRatio.model10Levels$Level

## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## V.TaxRatio.model10Levels$Level, V.TaxRatio.model10Levels$Var2

## Warning in TukeyHSD.aov(aov(V.TaxRatio.model10Levels$value ~
## V.TaxRatio.model10Levels$Level * : 'which' specified some non-factors which will
## be dropped

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = V.TaxRatio.model10Levels$value ~ V.TaxRatio.model10Levels$Level * V.TaxRatio.model10Levels$Var2)
## 
## $`V.TaxRatio.model10Levels$Var2`
##                        diff        lwr       upr     p adj
## QSeq0.5-raw     -6189.17356 -20176.266  7797.919 0.8446855
## QSeq1-raw       -2208.53837 -16195.630 11778.554 0.9991942
## QSeq2-raw       -1986.39590 -15973.488 12000.696 0.9995616
## QSeq3-raw       -1774.36718 -15761.459 12212.725 0.9997720
## QSeq10-raw      -1873.42510 -15860.517 12113.667 0.9996875
## QSeq100-raw     -1850.20400 -15837.296 12136.888 0.9997093
## QSeq1-QSeq0.5    3980.63519 -10006.457 17967.727 0.9798212
## QSeq2-QSeq0.5    4202.77766  -9784.314 18189.870 0.9734370
## QSeq3-QSeq0.5    4414.80638  -9572.286 18401.898 0.9660820
## QSeq10-QSeq0.5   4315.74846  -9671.344 18302.841 0.9696793
## QSeq100-QSeq0.5  4338.96956  -9648.123 18326.062 0.9688618
## QSeq2-QSeq1       222.14247 -13764.950 14209.235 1.0000000
## QSeq3-QSeq1       434.17119 -13552.921 14421.263 0.9999999
## QSeq10-QSeq1      335.11326 -13651.979 14322.205 1.0000000
## QSeq100-QSeq1     358.33437 -13628.758 14345.426 1.0000000
## QSeq3-QSeq2       212.02872 -13775.063 14199.121 1.0000000
## QSeq10-QSeq2      112.97080 -13874.121 14100.063 1.0000000
## QSeq100-QSeq2     136.19190 -13850.900 14123.284 1.0000000
## QSeq10-QSeq3      -99.05792 -14086.150 13888.034 1.0000000
## QSeq100-QSeq3     -75.83682 -14062.929 13911.255 1.0000000
## QSeq100-QSeq10     23.22111 -13963.871 14010.313 1.0000000

#leveneTest(value~as.factor(Level), data=V.TaxRatio.model10.p)

Now let’s look at a common community level statistic. PERMANOVA outputs:

# get permanova geography ####


model10A.Permanova.model<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.A,method2, "CategoryRratio"))
model10A.Permanova.env1<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.A, method2, "F1Rratio"))
model10A.Permanova.env2<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.A, method2, "F2Rratio"))
model10A.Permanova.env3<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.A, method2, "F3Rratio"))
model10A.Permanova.env4<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.A, method2, "F4Rratio"))
model10A.Permanova.env5<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.A,method2, "F5Rratio"))


model10B.Permanova.model<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.B, method2, "CategoryRratio"))
model10B.Permanova.env1<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.B, method2, "F1Rratio"))
model10B.Permanova.env2<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.B, method2, "F2Rratio"))
model10B.Permanova.env3<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.B, method2, "F3Rratio"))
model10B.Permanova.env4<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.B, method2, "F4Rratio"))
model10B.Permanova.env5<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.B, method2, "F5Rratio"))


model10C.Permanova.model<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C, method2, "CategoryRratio"))
model10C.Permanova.env1<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C, method2, "F1Rratio"))
model10C.Permanova.env2<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C, method2, "F2Rratio"))
model10C.Permanova.env3<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C, method2, "F3Rratio"))
model10C.Permanova.env4<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C, method2, "F4Rratio"))
model10C.Permanova.env5<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C, method2, "F5Rratio"))


model10D.Permanova.model<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.D, method2, "CategoryRratio"))
model10D.Permanova.env1<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.D, method2, "F1Rratio"))
model10D.Permanova.env2<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.D, method2, "F2Rratio"))
model10D.Permanova.env3<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.D, method2, "F3Rratio"))
model10D.Permanova.env4<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.D, method2, "F4Rratio"))
model10D.Permanova.env5<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.D, method2, "F5Rratio"))

model10A.Permanova.model$Level<-c(rep(1,10))
model10A.Permanova.env1$Level<-c(rep(1,10))
model10A.Permanova.env2$Level<-c(rep(1,10))
model10A.Permanova.env3$Level<-c(rep(1,10))
model10A.Permanova.env4$Level<-c(rep(1,10))
model10A.Permanova.env5$Level<-c(rep(1,10))

model10B.Permanova.model$Level<-c(rep(2,10))
model10B.Permanova.env1$Level<-c(rep(2,10))
model10B.Permanova.env2$Level<-c(rep(2,10))
model10B.Permanova.env3$Level<-c(rep(2,10))
model10B.Permanova.env4$Level<-c(rep(2,10))
model10B.Permanova.env5$Level<-c(rep(2,10))

model10C.Permanova.model$Level<-c(rep(3,10))
model10C.Permanova.env1$Level<-c(rep(3,10))
model10C.Permanova.env2$Level<-c(rep(3,10))
model10C.Permanova.env3$Level<-c(rep(3,10))
model10C.Permanova.env4$Level<-c(rep(3,10))
model10C.Permanova.env5$Level<-c(rep(3,10))

model10D.Permanova.model$Level<-c(rep(4,10))
model10D.Permanova.env1$Level<-c(rep(4,10))
model10D.Permanova.env2$Level<-c(rep(4,10))
model10D.Permanova.env3$Level<-c(rep(4,10))
model10D.Permanova.env4$Level<-c(rep(4,10))
model10D.Permanova.env5$Level<-c(rep(4,10))

permanova.model10Levels.model<-do.call("rbind", list(model10A.Permanova.model,model10B.Permanova.model,model10C.Permanova.model,model10D.Permanova.model))
permanova.model10Levels.env1<-do.call("rbind", list(model10A.Permanova.env1,model10B.Permanova.env1,model10C.Permanova.env1,model10D.Permanova.env1))
permanova.model10Levels.env2<-do.call("rbind", list(model10A.Permanova.env2,model10B.Permanova.env2,model10C.Permanova.env2,model10D.Permanova.env2))
permanova.model10Levels.env3<-do.call("rbind", list(model10A.Permanova.env3,model10B.Permanova.env3,model10C.Permanova.env3,model10D.Permanova.env3))
permanova.model10Levels.env4<-do.call("rbind", list(model10A.Permanova.env4,model10B.Permanova.env4,model10C.Permanova.env4,model10D.Permanova.env4))
permanova.model10Levels.env5<-do.call("rbind", list(model10A.Permanova.env5,model10B.Permanova.env5,model10C.Permanova.env5,model10D.Permanova.env5))

permanova.model10Levels.model<-melt(permanova.model10Levels.model, id.vars = "Level", measure.vars = method2)
permanova.model10Levels.env1<-melt(permanova.model10Levels.env1, id.vars = "Level", measure.vars = method2)
permanova.model10Levels.env2<-melt(permanova.model10Levels.env2, id.vars = "Level", measure.vars = method2)
permanova.model10Levels.env3<-melt(permanova.model10Levels.env3, id.vars = "Level", measure.vars = method2)
permanova.model10Levels.env4<-melt(permanova.model10Levels.env4, id.vars = "Level", measure.vars = method2)
permanova.model10Levels.env5<-melt(permanova.model10Levels.env5, id.vars = "Level", measure.vars = method2)

permanova.model10Levels.modelP<-data_summary2(permanova.model10Levels.model, varname="value", groupnames=c("Level", "variable"))
permanova.model10Levels.env1P<-data_summary2(permanova.model10Levels.env1, varname="value", groupnames=c("Level", "variable"))
permanova.model10Levels.env2P<-data_summary2(permanova.model10Levels.env2, varname="value", groupnames=c("Level", "variable"))
permanova.model10Levels.env3P<-data_summary2(permanova.model10Levels.env3, varname="value", groupnames=c("Level", "variable"))
permanova.model10Levels.env4P<-data_summary2(permanova.model10Levels.env4, varname="value", groupnames=c("Level", "variable"))
permanova.model10Levels.env5P<-data_summary2(permanova.model10Levels.env5, varname="value", groupnames=c("Level", "variable"))


ggplot(permanova.model10Levels.modelP, aes(x=Level, y=value, group = variable, color=variable))+
  geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(.3)) +
  scale_colour_viridis_d(direction=-1)+
  geom_line(position=position_dodge(.3))+
  geom_point(position=position_dodge(.3))+
  xlab("Degree of Structure")+
  ylab("Permanova modelRatio (Median +/- min/max)")+
  theme_classic()

ggplot(permanova.model10Levels.env1P, aes(x=Level, y=value, group = variable, color=variable))+
  geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(.3)) +
  scale_colour_viridis_d(direction=-1)+
  geom_line(position=position_dodge(.3))+
  geom_point(position=position_dodge(.3))+
  xlab("Degree of Structure")+
  ylab("Permanova env1Ratio (Median +/- min/max)")+
  theme_classic()

ggplot(permanova.model10Levels.env2P, aes(x=Level, y=value, group = variable, color=variable))+
  geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(.3)) +
  scale_colour_viridis_d(direction=-1)+
  geom_line(position=position_dodge(.3))+
  geom_point(position=position_dodge(.3))+
  xlab("Degree of Structure")+
  ylab("Permanova env2Ratio (Median +/- min/max)")+
  theme_classic()

ggplot(permanova.model10Levels.env3P, aes(x=Level, y=value, group = variable, color=variable))+
  geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(.3)) +
  scale_colour_viridis_d(direction=-1)+
  geom_line(position=position_dodge(.3))+
  geom_point(position=position_dodge(.3))+
  xlab("Degree of Structure")+
  ylab("Permanova env3Ratio (Median +/- min/max)")+
  theme_classic()

ggplot(permanova.model10Levels.env4P, aes(x=Level, y=value, group = variable, color=variable))+
  geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(.3)) +
  scale_colour_viridis_d(direction=-1)+
  geom_line(position=position_dodge(.3))+
  geom_point(position=position_dodge(.3))+
  xlab("Degree of Structure")+
  ylab("Permanova env4Ratio (Median +/- min/max)")+
  theme_classic()

ggplot(permanova.model10Levels.env5P, aes(x=Level, y=value, group = variable, color=variable))+
  geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(.3)) +
  scale_colour_viridis_d(direction=-1)+
  geom_line(position=position_dodge(.3))+
  geom_point(position=position_dodge(.3))+
  xlab("Degree of Structure")+
  ylab("Permanova env5Ratio (Median +/- min/max)")+
  theme_classic()

permanova.model10Levels.modelP1<-data_summary(permanova.model10Levels.model, varname="value", groupnames=c("Level", "variable"))
permanova.model10Levels.env1P1<-data_summary(permanova.model10Levels.env1, varname="value", groupnames=c("Level", "variable"))
permanova.model10Levels.env2P1<-data_summary(permanova.model10Levels.env2, varname="value", groupnames=c("Level", "variable"))
permanova.model10Levels.env3P1<-data_summary(permanova.model10Levels.env3, varname="value", groupnames=c("Level", "variable"))
permanova.model10Levels.env4P1<-data_summary(permanova.model10Levels.env4, varname="value", groupnames=c("Level", "variable"))
permanova.model10Levels.env5P1<-data_summary(permanova.model10Levels.env5, varname="value", groupnames=c("Level", "variable"))


ggplot(permanova.model10Levels.modelP1, aes(x=Level, y=value, group = variable, color=variable))+
  geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.3)) +
  scale_colour_viridis_d(direction=-1)+
  geom_line(position=position_dodge(.3))+
  geom_point(position=position_dodge(.3))+
  xlab("Degree of Structure")+
  ylab("Permanova modelRatio (Mean +/- sd)")+
  theme_classic()

ggplot(permanova.model10Levels.env1P1, aes(x=Level, y=value, group = variable, color=variable))+
  geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.3)) +
  scale_colour_viridis_d(direction=-1)+
  geom_line(position=position_dodge(.3))+
  geom_point(position=position_dodge(.3))+
  xlab("Degree of Structure")+
  ylab("Permanova env1Ratio (Mean +/- sd)")+
  theme_classic()

ggplot(permanova.model10Levels.env2P1, aes(x=Level, y=value, group = variable, color=variable))+
  geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.3)) +
  scale_colour_viridis_d(direction=-1)+
  geom_line(position=position_dodge(.3))+
  geom_point(position=position_dodge(.3))+
  xlab("Degree of Structure")+
  ylab("Permanova env2Ratio (Mean +/- sd)")+
  theme_classic()

ggplot(permanova.model10Levels.env3P1, aes(x=Level, y=value, group = variable, color=variable))+
  geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.3)) +
  scale_colour_viridis_d(direction=-1)+
  geom_line(position=position_dodge(.3))+
  geom_point(position=position_dodge(.3))+
  xlab("Degree of Structure")+
  ylab("Permanova env3Ratio (Mean +/- sd)")+
  theme_classic()

ggplot(permanova.model10Levels.env4P1, aes(x=Level, y=value, group = variable, color=variable))+
  geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.3)) +
  scale_colour_viridis_d(direction=-1)+
  geom_line(position=position_dodge(.3))+
  geom_point(position=position_dodge(.3))+
  xlab("Degree of Structure")+
  ylab("Permanova env4Ratio (Mean +/- sd)")+
  theme_classic()

ggplot(permanova.model10Levels.env5P1, aes(x=Level, y=value, group = variable, color=variable))+
  geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.3)) +
  scale_colour_viridis_d(direction=-1)+
  geom_line(position=position_dodge(.3))+
  geom_point(position=position_dodge(.3))+
  xlab("Degree of Structure")+
  ylab("Permanova env5Ratio (Mean +/- sd)")+
  theme_classic()

PERMANOVA results are very consistent: the statistical model is typically captured equally well across normalization methods. However, QSeq methods significantly increase the accuracy of relating specific environmental gradients to the community structure.

Statistics:

summary(aov(permanova.model10Levels.model$value~permanova.model10Levels.model$Level*permanova.model10Levels.model$variable))

##                                                                             Df
## permanova.model10Levels.model$Level                                          1
## permanova.model10Levels.model$variable                                       6
## permanova.model10Levels.model$Level:permanova.model10Levels.model$variable   6
## Residuals                                                                  266
##                                                                             Sum Sq
## permanova.model10Levels.model$Level                                        0.03567
## permanova.model10Levels.model$variable                                     0.00002
## permanova.model10Levels.model$Level:permanova.model10Levels.model$variable 0.00011
## Residuals                                                                  0.07067
##                                                                            Mean Sq
## permanova.model10Levels.model$Level                                        0.03567
## permanova.model10Levels.model$variable                                     0.00000
## permanova.model10Levels.model$Level:permanova.model10Levels.model$variable 0.00002
## Residuals                                                                  0.00027
##                                                                            F value
## permanova.model10Levels.model$Level                                        134.269
## permanova.model10Levels.model$variable                                       0.010
## permanova.model10Levels.model$Level:permanova.model10Levels.model$variable   0.068
## Residuals                                                                         
##                                                                            Pr(>F)
## permanova.model10Levels.model$Level                                        <2e-16
## permanova.model10Levels.model$variable                                      1.000
## permanova.model10Levels.model$Level:permanova.model10Levels.model$variable  0.999
## Residuals                                                                        
##                                                                               
## permanova.model10Levels.model$Level                                        ***
## permanova.model10Levels.model$variable                                        
## permanova.model10Levels.model$Level:permanova.model10Levels.model$variable    
## Residuals                                                                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

summary(aov(permanova.model10Levels.env1$value~permanova.model10Levels.env1$Level*permanova.model10Levels.env1$variable))

##                                                                           Df
## permanova.model10Levels.env1$Level                                         1
## permanova.model10Levels.env1$variable                                      6
## permanova.model10Levels.env1$Level:permanova.model10Levels.env1$variable   6
## Residuals                                                                266
##                                                                          Sum Sq
## permanova.model10Levels.env1$Level                                       0.0147
## permanova.model10Levels.env1$variable                                    0.1168
## permanova.model10Levels.env1$Level:permanova.model10Levels.env1$variable 0.0216
## Residuals                                                                2.5369
##                                                                           Mean Sq
## permanova.model10Levels.env1$Level                                       0.014673
## permanova.model10Levels.env1$variable                                    0.019473
## permanova.model10Levels.env1$Level:permanova.model10Levels.env1$variable 0.003593
## Residuals                                                                0.009537
##                                                                          F value
## permanova.model10Levels.env1$Level                                         1.538
## permanova.model10Levels.env1$variable                                      2.042
## permanova.model10Levels.env1$Level:permanova.model10Levels.env1$variable   0.377
## Residuals                                                                       
##                                                                          Pr(>F)
## permanova.model10Levels.env1$Level                                       0.2159
## permanova.model10Levels.env1$variable                                    0.0605
## permanova.model10Levels.env1$Level:permanova.model10Levels.env1$variable 0.8935
## Residuals                                                                      
##                                                                           
## permanova.model10Levels.env1$Level                                        
## permanova.model10Levels.env1$variable                                    .
## permanova.model10Levels.env1$Level:permanova.model10Levels.env1$variable  
## Residuals                                                                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

summary(aov(permanova.model10Levels.env2$value~permanova.model10Levels.env2$Level*permanova.model10Levels.env2$variable))

##                                                                           Df
## permanova.model10Levels.env2$Level                                         1
## permanova.model10Levels.env2$variable                                      6
## permanova.model10Levels.env2$Level:permanova.model10Levels.env2$variable   6
## Residuals                                                                266
##                                                                          Sum Sq
## permanova.model10Levels.env2$Level                                       0.2725
## permanova.model10Levels.env2$variable                                    2.4442
## permanova.model10Levels.env2$Level:permanova.model10Levels.env2$variable 0.9495
## Residuals                                                                1.3632
##                                                                          Mean Sq
## permanova.model10Levels.env2$Level                                        0.2725
## permanova.model10Levels.env2$variable                                     0.4074
## permanova.model10Levels.env2$Level:permanova.model10Levels.env2$variable  0.1582
## Residuals                                                                 0.0051
##                                                                          F value
## permanova.model10Levels.env2$Level                                         53.16
## permanova.model10Levels.env2$variable                                      79.49
## permanova.model10Levels.env2$Level:permanova.model10Levels.env2$variable   30.88
## Residuals                                                                       
##                                                                            Pr(>F)
## permanova.model10Levels.env2$Level                                       3.51e-12
## permanova.model10Levels.env2$variable                                     < 2e-16
## permanova.model10Levels.env2$Level:permanova.model10Levels.env2$variable  < 2e-16
## Residuals                                                                        
##                                                                             
## permanova.model10Levels.env2$Level                                       ***
## permanova.model10Levels.env2$variable                                    ***
## permanova.model10Levels.env2$Level:permanova.model10Levels.env2$variable ***
## Residuals                                                                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

summary(aov(permanova.model10Levels.env3$value~permanova.model10Levels.env3$Level*permanova.model10Levels.env3$variable))

##                                                                           Df
## permanova.model10Levels.env3$Level                                         1
## permanova.model10Levels.env3$variable                                      6
## permanova.model10Levels.env3$Level:permanova.model10Levels.env3$variable   6
## Residuals                                                                266
##                                                                          Sum Sq
## permanova.model10Levels.env3$Level                                       0.2745
## permanova.model10Levels.env3$variable                                    1.2035
## permanova.model10Levels.env3$Level:permanova.model10Levels.env3$variable 0.1164
## Residuals                                                                1.2358
##                                                                          Mean Sq
## permanova.model10Levels.env3$Level                                       0.27454
## permanova.model10Levels.env3$variable                                    0.20058
## permanova.model10Levels.env3$Level:permanova.model10Levels.env3$variable 0.01940
## Residuals                                                                0.00465
##                                                                          F value
## permanova.model10Levels.env3$Level                                        59.094
## permanova.model10Levels.env3$variable                                     43.175
## permanova.model10Levels.env3$Level:permanova.model10Levels.env3$variable   4.176
## Residuals                                                                       
##                                                                            Pr(>F)
## permanova.model10Levels.env3$Level                                       2.91e-13
## permanova.model10Levels.env3$variable                                     < 2e-16
## permanova.model10Levels.env3$Level:permanova.model10Levels.env3$variable 0.000496
## Residuals                                                                        
##                                                                             
## permanova.model10Levels.env3$Level                                       ***
## permanova.model10Levels.env3$variable                                    ***
## permanova.model10Levels.env3$Level:permanova.model10Levels.env3$variable ***
## Residuals                                                                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

summary(aov(permanova.model10Levels.env4$value~permanova.model10Levels.env4$Level*permanova.model10Levels.env4$variable))

##                                                                           Df
## permanova.model10Levels.env4$Level                                         1
## permanova.model10Levels.env4$variable                                      6
## permanova.model10Levels.env4$Level:permanova.model10Levels.env4$variable   6
## Residuals                                                                266
##                                                                          Sum Sq
## permanova.model10Levels.env4$Level                                        0.200
## permanova.model10Levels.env4$variable                                     0.309
## permanova.model10Levels.env4$Level:permanova.model10Levels.env4$variable  0.067
## Residuals                                                                 6.642
##                                                                          Mean Sq
## permanova.model10Levels.env4$Level                                       0.20019
## permanova.model10Levels.env4$variable                                    0.05156
## permanova.model10Levels.env4$Level:permanova.model10Levels.env4$variable 0.01114
## Residuals                                                                0.02497
##                                                                          F value
## permanova.model10Levels.env4$Level                                         8.017
## permanova.model10Levels.env4$variable                                      2.065
## permanova.model10Levels.env4$Level:permanova.model10Levels.env4$variable   0.446
## Residuals                                                                       
##                                                                           Pr(>F)
## permanova.model10Levels.env4$Level                                       0.00499
## permanova.model10Levels.env4$variable                                    0.05764
## permanova.model10Levels.env4$Level:permanova.model10Levels.env4$variable 0.84738
## Residuals                                                                       
##                                                                            
## permanova.model10Levels.env4$Level                                       **
## permanova.model10Levels.env4$variable                                    . 
## permanova.model10Levels.env4$Level:permanova.model10Levels.env4$variable   
## Residuals                                                                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

summary(aov(permanova.model10Levels.env5$value~permanova.model10Levels.env5$Level*permanova.model10Levels.env5$variable))

##                                                                           Df
## permanova.model10Levels.env5$Level                                         1
## permanova.model10Levels.env5$variable                                      6
## permanova.model10Levels.env5$Level:permanova.model10Levels.env5$variable   6
## Residuals                                                                266
##                                                                          Sum Sq
## permanova.model10Levels.env5$Level                                        0.000
## permanova.model10Levels.env5$variable                                     0.889
## permanova.model10Levels.env5$Level:permanova.model10Levels.env5$variable  0.412
## Residuals                                                                31.097
##                                                                          Mean Sq
## permanova.model10Levels.env5$Level                                       0.00006
## permanova.model10Levels.env5$variable                                    0.14819
## permanova.model10Levels.env5$Level:permanova.model10Levels.env5$variable 0.06860
## Residuals                                                                0.11691
##                                                                          F value
## permanova.model10Levels.env5$Level                                         0.001
## permanova.model10Levels.env5$variable                                      1.268
## permanova.model10Levels.env5$Level:permanova.model10Levels.env5$variable   0.587
## Residuals                                                                       
##                                                                          Pr(>F)
## permanova.model10Levels.env5$Level                                        0.982
## permanova.model10Levels.env5$variable                                     0.273
## permanova.model10Levels.env5$Level:permanova.model10Levels.env5$variable  0.741
## Residuals

leveneTest(permanova.model10Levels.model$value~permanova.model10Levels.model$variable)

## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value Pr(>F)
## group   6  0.0018      1
##       273

leveneTest(permanova.model10Levels.env1$value~permanova.model10Levels.env1$variable)

## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value    Pr(>F)    
## group   6  12.249 3.331e-12 ***
##       273                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

leveneTest(permanova.model10Levels.env2$value~permanova.model10Levels.env2$variable)

## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value    Pr(>F)    
## group   6  36.543 < 2.2e-16 ***
##       273                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

leveneTest(permanova.model10Levels.env3$value~permanova.model10Levels.env3$variable)

## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value    Pr(>F)    
## group   6   25.85 < 2.2e-16 ***
##       273                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

leveneTest(permanova.model10Levels.env4$value~permanova.model10Levels.env4$variable)

## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value    Pr(>F)    
## group   6  22.639 < 2.2e-16 ***
##       273                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

leveneTest(permanova.model10Levels.env5$value~permanova.model10Levels.env5$variable)

## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value    Pr(>F)    
## group   6  7.4037 2.356e-07 ***
##       273                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Expt 2: Normalization vs Sequencing Depth

Let’s say we want to know the effect of undersampling interacts with our normalization protocol to affect our ability to detect relationships between taxa and the environment. We can vary the sequencing depth:

# make sequencing depth ####
#method<-c("QSeq0.5", "QSeq1", "QSeq2", "QSeq3", "QSeq10")
model10.C1<-BENCHMARK.MM(reps=10, commonN=20, groupN=20, singleN=15, D=100, V=50, method)

model10.C2<-BENCHMARK.MM(reps=10, commonN=20, groupN=20, singleN=15, D=200, V=100, method)

model10.C3<-BENCHMARK.MM(reps=10, commonN=20, groupN=20, singleN=15, D=500, V=250, method)

model10.C4<-BENCHMARK.MM(reps=10, commonN=20, groupN=20, singleN=15, D=1000, V=500, method)

model10.C5<-BENCHMARK.MM(reps=10, commonN=20, groupN=20, singleN=15, D=2000, V=1000, method)

LII output:

SummaryLII.model10.C1<-as.data.frame(Summarize.LII(model10.C1,method2))
SummaryLII.model10.C2<-as.data.frame(Summarize.LII(model10.C2, method2)) 
SummaryLII.model10.C3<-as.data.frame(Summarize.LII(model10.C3, method2))
SummaryLII.model10.C4<-as.data.frame(Summarize.LII(model10.C4, method2))
SummaryLII.model10.C5<-as.data.frame(Summarize.LII(model10.C5, method2))
# prepare data for merging datasets
SummaryLII.model10.C1$Level<-c(rep(100,10))
SummaryLII.model10.C1<-melt(SummaryLII.model10.C1, id.vars = "Level", measure.vars = method2)
SummaryLII.model10.C2$Level<-c(rep(200,10))
SummaryLII.model10.C2<-melt(SummaryLII.model10.C2, id.vars = "Level", measure.vars = method2)
SummaryLII.model10.C3$Level<-c(rep(500,10))
SummaryLII.model10.C3<-melt(SummaryLII.model10.C3, id.vars = "Level", measure.vars = method2)
SummaryLII.model10.C4$Level<-c(rep(1000,10))
SummaryLII.model10.C4<-melt(SummaryLII.model10.C4, id.vars = "Level", measure.vars = method2)
SummaryLII.model10.C5$Level<-c(rep(2000,10))
SummaryLII.model10.C5<-melt(SummaryLII.model10.C5, id.vars = "Level", measure.vars = method2)
# merge datasets
model10.SeqLevels<-do.call("rbind", list(SummaryLII.model10.C1,SummaryLII.model10.C2,SummaryLII.model10.C3,SummaryLII.model10.C4,SummaryLII.model10.C5))

# summarize for plotting
model10.SeqLevels.summary<-data_summary(model10.SeqLevels, varname="value", groupnames=c("Level", "variable"))
model10.SeqLevels.summary2<-data_summary2(model10.SeqLevels, varname="value", groupnames=c("Level", "variable"))

# plot
ggplot(model10.SeqLevels.summary, aes(x=Level, y=value, group = variable, color=variable))+
  geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(30)) +
  scale_colour_viridis_d(direction=-1)+
  geom_line(position=position_dodge(30))+
  geom_point(position=position_dodge(30))+
  xlab("Sequencing Depth")+
  ylab("LII Value (Mean +/- sd)")+
  theme_classic()

ggplot(model10.SeqLevels.summary2, aes(x=Level, y=value, group = variable, color=variable))+
  geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(30)) +
  scale_colour_viridis_d(direction=-1)+
  geom_line(position=position_dodge(30))+
  geom_point(position=position_dodge(30))+
  xlab("Sequencing Depth")+
  ylab("LII Value (Median +/- min/max)")+
  theme_classic()

These results are consistent with our previous experiment, where QSeq2-100 lose the least information; QSeq0.5 generally performs the worst, and un-normalized data only loses more information than QSeq0.5 and under certain conditions QSeq1. All methods perform best at highest sequencing depth.

Now let’s look at how well the environmental gradients predicts taxon abundance:

# sequencing depth env. lm ratio ####
SM.lmRatio.model10.C1<-as.data.frame(Summarize.lmRatiotab.Median(model10.C1,method2))
SV.lmRatio.model10.C1<-as.data.frame(Summarize.lmRatiotab.Var(model10.C1,method2))
SM.lmRatio.model10.C2<-as.data.frame(Summarize.lmRatiotab.Median(model10.C2,method2))
SV.lmRatio.model10.C2<-as.data.frame(Summarize.lmRatiotab.Var(model10.C2,method2))
SM.lmRatio.model10.C3<-as.data.frame(Summarize.lmRatiotab.Median(model10.C3,method2))
SV.lmRatio.model10.C3<-as.data.frame(Summarize.lmRatiotab.Var(model10.C3,method2))
SM.lmRatio.model10.C4<-as.data.frame(Summarize.lmRatiotab.Median(model10.C4,method2))
SV.lmRatio.model10.C4<-as.data.frame(Summarize.lmRatiotab.Var(model10.C4,method2))
SM.lmRatio.model10.C5<-as.data.frame(Summarize.lmRatiotab.Median(model10.C5,method2))
SV.lmRatio.model10.C5<-as.data.frame(Summarize.lmRatiotab.Var(model10.C5,method2))
# prepare data for merging datasets

SM.lmRatio.model10.C1$Level<-c(rep(100,10))
SV.lmRatio.model10.C1$Level<-c(rep(100,10))
SM.lmRatio.model10.C2$Level<-c(rep(200,10))
SV.lmRatio.model10.C2$Level<-c(rep(200,10))
SM.lmRatio.model10.C3$Level<-c(rep(500,10))
SV.lmRatio.model10.C3$Level<-c(rep(500,10))
SM.lmRatio.model10.C4$Level<-c(rep(1000,10))
SV.lmRatio.model10.C4$Level<-c(rep(1000,10))
SM.lmRatio.model10.C5$Level<-c(rep(2000,10))
SV.lmRatio.model10.C5$Level<-c(rep(2000,10))

SM.lmRatio.model10.C1<-melt(SM.lmRatio.model10.C1, id.vars = "Level", measure.vars = method2)
SV.lmRatio.model10.C1<-melt(SV.lmRatio.model10.C1, id.vars = "Level", measure.vars = method2)
SM.lmRatio.model10.C2<-melt(SM.lmRatio.model10.C2, id.vars = "Level", measure.vars = method2)
SV.lmRatio.model10.C2<-melt(SV.lmRatio.model10.C2, id.vars = "Level", measure.vars = method2)
SM.lmRatio.model10.C3<-melt(SM.lmRatio.model10.C3, id.vars = "Level", measure.vars = method2)
SV.lmRatio.model10.C3<-melt(SV.lmRatio.model10.C3, id.vars = "Level", measure.vars = method2)
SM.lmRatio.model10.C4<-melt(SM.lmRatio.model10.C4, id.vars = "Level", measure.vars = method2)
SV.lmRatio.model10.C4<-melt(SV.lmRatio.model10.C4, id.vars = "Level", measure.vars = method2)
SM.lmRatio.model10.C5<-melt(SM.lmRatio.model10.C5, id.vars = "Level", measure.vars = method2)
SV.lmRatio.model10.C5<-melt(SV.lmRatio.model10.C5, id.vars = "Level", measure.vars = method2)

# merge datasets
SM.lmRatio.model10.CLevels<-do.call("rbind", list(SM.lmRatio.model10.C1,SM.lmRatio.model10.C2,SM.lmRatio.model10.C3,SM.lmRatio.model10.C4, SM.lmRatio.model10.C5))
SV.lmRatio.model10.CLevels<-do.call("rbind", list(SV.lmRatio.model10.C1,SV.lmRatio.model10.C2,SV.lmRatio.model10.C3,SV.lmRatio.model10.C4, SV.lmRatio.model10.C5))


# summarize for plotting
SM.lmRatio.model10C.p<-data_summary(SM.lmRatio.model10.CLevels, varname="value", groupnames=c("Level", "variable"))
SV.lmRatio.model10C.p<-data_summary(SV.lmRatio.model10.CLevels, varname="value", groupnames=c("Level", "variable"))
# plot

SM.lmRatio.model10C.p2<-data_summary2(SM.lmRatio.model10.CLevels, varname="value", groupnames=c("Level", "variable"))
SV.lmRatio.model10C.p2<-data_summary2(SV.lmRatio.model10.CLevels, varname="value", groupnames=c("Level", "variable"))
# plot
ggplot(SM.lmRatio.model10C.p, aes(x=Level, y=value, group = variable, color=variable))+
  geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(30)) +
  scale_color_viridis_d(direction=-1)+
  geom_line(position=position_dodge(30))+
  geom_point(position=position_dodge(30))+
  xlab("Sampling Depth")+
  ylab("Median lmRatio (Mean +/- sd)")+
  theme_classic()

ggplot(SV.lmRatio.model10C.p, aes(x=Level, y=value, group = variable, color=variable))+
  geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(30)) +
  scale_color_viridis_d(direction=-1)+
  geom_line(position=position_dodge(30))+
  geom_point(position=position_dodge(30))+
  xlab("Sampling Depth")+
  ylab("Variance lmRatio (Mean +/- sd)")+
  theme_classic()

ggplot(SM.lmRatio.model10C.p2, aes(x=Level, y=value, group = variable, color=variable))+
  geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(30)) +
  scale_color_viridis_d(direction=-1)+
  geom_line(position=position_dodge(30))+
  geom_point(position=position_dodge(30))+
  xlab("Sampling Depth")+
  ylab("Median lmRatio (Median +/- min/max)")+
  theme_classic()

ggplot(SV.lmRatio.model10C.p2, aes(x=Level, y=value, group = variable, color=variable))+
  geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(30)) +
  scale_color_viridis_d(direction=-1)+
  geom_line(position=position_dodge(30))+
  geom_point(position=position_dodge(30))+
  xlab("Sampling Depth")+
  ylab("Variance lmRatio (Median +/- min/max)")+
  theme_classic()

Typcially QSeq0.5 performs poorly, while other methods are essentially comparable. Often at low sequencing depth, un-normalized data has a performance that is somewhere between the QSeq1 and QSeq0.5 data. In some runs of the simulation it is a significant effect, in others it is not.

summary(aov(SM.lmRatio.model10.CLevels$value~SM.lmRatio.model10.CLevels$Level*SM.lmRatio.model10.CLevels$variable))

##                                                                       Df
## SM.lmRatio.model10.CLevels$Level                                       1
## SM.lmRatio.model10.CLevels$variable                                    6
## SM.lmRatio.model10.CLevels$Level:SM.lmRatio.model10.CLevels$variable   6
## Residuals                                                            336
##                                                                       Sum Sq
## SM.lmRatio.model10.CLevels$Level                                     0.00827
## SM.lmRatio.model10.CLevels$variable                                  0.04372
## SM.lmRatio.model10.CLevels$Level:SM.lmRatio.model10.CLevels$variable 0.03204
## Residuals                                                            0.19790
##                                                                       Mean Sq
## SM.lmRatio.model10.CLevels$Level                                     0.008267
## SM.lmRatio.model10.CLevels$variable                                  0.007286
## SM.lmRatio.model10.CLevels$Level:SM.lmRatio.model10.CLevels$variable 0.005340
## Residuals                                                            0.000589
##                                                                      F value
## SM.lmRatio.model10.CLevels$Level                                      14.036
## SM.lmRatio.model10.CLevels$variable                                   12.371
## SM.lmRatio.model10.CLevels$Level:SM.lmRatio.model10.CLevels$variable   9.067
## Residuals                                                                   
##                                                                        Pr(>F)
## SM.lmRatio.model10.CLevels$Level                                     0.000211
## SM.lmRatio.model10.CLevels$variable                                  1.36e-12
## SM.lmRatio.model10.CLevels$Level:SM.lmRatio.model10.CLevels$variable 3.37e-09
## Residuals                                                                    
##                                                                         
## SM.lmRatio.model10.CLevels$Level                                     ***
## SM.lmRatio.model10.CLevels$variable                                  ***
## SM.lmRatio.model10.CLevels$Level:SM.lmRatio.model10.CLevels$variable ***
## Residuals                                                               
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

TukeyHSD(aov(SM.lmRatio.model10.CLevels$value~SM.lmRatio.model10.CLevels$Level*SM.lmRatio.model10.CLevels$variable))

## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## SM.lmRatio.model10.CLevels$Level

## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## SM.lmRatio.model10.CLevels$Level, SM.lmRatio.model10.CLevels$variable

## Warning in TukeyHSD.aov(aov(SM.lmRatio.model10.CLevels$value ~
## SM.lmRatio.model10.CLevels$Level * : 'which' specified some non-factors which
## will be dropped

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = SM.lmRatio.model10.CLevels$value ~ SM.lmRatio.model10.CLevels$Level * SM.lmRatio.model10.CLevels$variable)
## 
## $`SM.lmRatio.model10.CLevels$variable`
##                          diff         lwr         upr     p adj
## QSeq0.5-raw     -3.277554e-02 -0.04717334 -0.01837774 0.0000000
## QSeq1-raw       -4.357810e-03 -0.01875561  0.01003999 0.9727401
## QSeq2-raw       -2.019430e-03 -0.01641723  0.01237837 0.9995974
## QSeq3-raw       -2.913451e-04 -0.01468914  0.01410645 1.0000000
## QSeq10-raw      -3.168551e-05 -0.01442949  0.01436611 1.0000000
## QSeq100-raw     -3.637026e-05 -0.01443417  0.01436143 1.0000000
## QSeq1-QSeq0.5    2.841773e-02  0.01401993  0.04281553 0.0000002
## QSeq2-QSeq0.5    3.075611e-02  0.01635831  0.04515391 0.0000000
## QSeq3-QSeq0.5    3.248419e-02  0.01808639  0.04688199 0.0000000
## QSeq10-QSeq0.5   3.274385e-02  0.01834605  0.04714165 0.0000000
## QSeq100-QSeq0.5  3.273917e-02  0.01834137  0.04713697 0.0000000
## QSeq2-QSeq1      2.338381e-03 -0.01205942  0.01673618 0.9990658
## QSeq3-QSeq1      4.066465e-03 -0.01033133  0.01846426 0.9808036
## QSeq10-QSeq1     4.326125e-03 -0.01007167  0.01872392 0.9737193
## QSeq100-QSeq1    4.321440e-03 -0.01007636  0.01871924 0.9738619
## QSeq3-QSeq2      1.728084e-03 -0.01266972  0.01612588 0.9998371
## QSeq10-QSeq2     1.987744e-03 -0.01241006  0.01638554 0.9996326
## QSeq100-QSeq2    1.983059e-03 -0.01241474  0.01638086 0.9996376
## QSeq10-QSeq3     2.596596e-04 -0.01413814  0.01465746 1.0000000
## QSeq100-QSeq3    2.549749e-04 -0.01414282  0.01465277 1.0000000
## QSeq100-QSeq10  -4.684748e-06 -0.01440248  0.01439311 1.0000000

summary(aov(SV.lmRatio.model10.CLevels$value~SV.lmRatio.model10.CLevels$Level*SV.lmRatio.model10.CLevels$variable))

##                                                                       Df Sum Sq
## SV.lmRatio.model10.CLevels$Level                                       1 0.2656
## SV.lmRatio.model10.CLevels$variable                                    6 0.3620
## SV.lmRatio.model10.CLevels$Level:SV.lmRatio.model10.CLevels$variable   6 0.0176
## Residuals                                                            336 2.5287
##                                                                      Mean Sq
## SV.lmRatio.model10.CLevels$Level                                     0.26562
## SV.lmRatio.model10.CLevels$variable                                  0.06033
## SV.lmRatio.model10.CLevels$Level:SV.lmRatio.model10.CLevels$variable 0.00294
## Residuals                                                            0.00753
##                                                                      F value
## SV.lmRatio.model10.CLevels$Level                                      35.295
## SV.lmRatio.model10.CLevels$variable                                    8.017
## SV.lmRatio.model10.CLevels$Level:SV.lmRatio.model10.CLevels$variable   0.390
## Residuals                                                                   
##                                                                        Pr(>F)
## SV.lmRatio.model10.CLevels$Level                                     7.08e-09
## SV.lmRatio.model10.CLevels$variable                                  4.24e-08
## SV.lmRatio.model10.CLevels$Level:SV.lmRatio.model10.CLevels$variable    0.885
## Residuals                                                                    
##                                                                         
## SV.lmRatio.model10.CLevels$Level                                     ***
## SV.lmRatio.model10.CLevels$variable                                  ***
## SV.lmRatio.model10.CLevels$Level:SV.lmRatio.model10.CLevels$variable    
## Residuals                                                               
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

TukeyHSD(aov(SV.lmRatio.model10.CLevels$value~SV.lmRatio.model10.CLevels$Level*SV.lmRatio.model10.CLevels$variable))

## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## SV.lmRatio.model10.CLevels$Level

## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## SV.lmRatio.model10.CLevels$Level, SV.lmRatio.model10.CLevels$variable

## Warning in TukeyHSD.aov(aov(SV.lmRatio.model10.CLevels$value ~
## SV.lmRatio.model10.CLevels$Level * : 'which' specified some non-factors which
## will be dropped

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = SV.lmRatio.model10.CLevels$value ~ SV.lmRatio.model10.CLevels$Level * SV.lmRatio.model10.CLevels$variable)
## 
## $`SV.lmRatio.model10.CLevels$variable`
##                          diff         lwr          upr     p adj
## QSeq0.5-raw      3.104695e-02 -0.02041918  0.082513070 0.5561473
## QSeq1-raw       -2.924599e-02 -0.08071212  0.022220129 0.6261669
## QSeq2-raw       -5.477231e-02 -0.10623844 -0.003306191 0.0286068
## QSeq3-raw       -5.303787e-02 -0.10450399 -0.001571746 0.0385466
## QSeq10-raw      -5.727050e-02 -0.10873662 -0.005804376 0.0182487
## QSeq100-raw     -5.720414e-02 -0.10867026 -0.005738015 0.0184735
## QSeq1-QSeq0.5   -6.029294e-02 -0.11175906 -0.008826818 0.0102743
## QSeq2-QSeq0.5   -8.581926e-02 -0.13728538 -0.034353137 0.0000246
## QSeq3-QSeq0.5   -8.408482e-02 -0.13555094 -0.032618692 0.0000394
## QSeq10-QSeq0.5  -8.831745e-02 -0.13978357 -0.036851323 0.0000123
## QSeq100-QSeq0.5 -8.825109e-02 -0.13971721 -0.036784962 0.0000125
## QSeq2-QSeq1     -2.552632e-02 -0.07699244  0.025939804 0.7617524
## QSeq3-QSeq1     -2.379187e-02 -0.07525800  0.027674249 0.8167894
## QSeq10-QSeq1    -2.802451e-02 -0.07949063  0.023441619 0.6726082
## QSeq100-QSeq1   -2.795814e-02 -0.07942427  0.023507980 0.6750902
## QSeq3-QSeq2      1.734445e-03 -0.04973168  0.053200569 0.9999999
## QSeq10-QSeq2    -2.498185e-03 -0.05396431  0.048967938 0.9999992
## QSeq100-QSeq2   -2.431824e-03 -0.05389795  0.049034299 0.9999993
## QSeq10-QSeq3    -4.232630e-03 -0.05569875  0.047233493 0.9999824
## QSeq100-QSeq3   -4.166269e-03 -0.05563239  0.047299854 0.9999840
## QSeq100-QSeq10   6.636112e-05 -0.05139976  0.051532485 1.0000000

leveneTest(value~as.factor(Level)*variable, data=SV.lmRatio.model10.CLevels)

## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value Pr(>F)
## group  34  1.0147   0.45
##       315

And same steps but for the categorical variables:

# lm ratio model sequencing depth ####
SM.lmRatioM.model10.C1<-as.data.frame(Summarize.lmRatiotabModel.Median(model10.C1,method2))
SV.lmRatioM.model10.C1<-as.data.frame(Summarize.lmRatiotabModel.Var(model10.C1,method2))
SM.lmRatioM.model10.C2<-as.data.frame(Summarize.lmRatiotabModel.Median(model10.C2,method2))
SV.lmRatioM.model10.C2<-as.data.frame(Summarize.lmRatiotabModel.Var(model10.C2,method2))
SM.lmRatioM.model10.C3<-as.data.frame(Summarize.lmRatiotabModel.Median(model10.C3,method2))
SV.lmRatioM.model10.C3<-as.data.frame(Summarize.lmRatiotabModel.Var(model10.C3,method2))
SM.lmRatioM.model10.C4<-as.data.frame(Summarize.lmRatiotabModel.Median(model10.C4,method2))
SV.lmRatioM.model10.C4<-as.data.frame(Summarize.lmRatiotabModel.Var(model10.C4,method2))
SM.lmRatioM.model10.C5<-as.data.frame(Summarize.lmRatiotabModel.Median(model10.C5,method2))
SV.lmRatioM.model10.C5<-as.data.frame(Summarize.lmRatiotabModel.Var(model10.C5,method2))
# prepare data for merging datasets

SM.lmRatioM.model10.C1$Level<-c(rep(100,10))
SV.lmRatioM.model10.C1$Level<-c(rep(100,10))
SM.lmRatioM.model10.C2$Level<-c(rep(200,10))
SV.lmRatioM.model10.C2$Level<-c(rep(200,10))
SM.lmRatioM.model10.C3$Level<-c(rep(500,10))
SV.lmRatioM.model10.C3$Level<-c(rep(500,10))
SM.lmRatioM.model10.C4$Level<-c(rep(1000,10))
SV.lmRatioM.model10.C4$Level<-c(rep(1000,10))
SM.lmRatioM.model10.C5$Level<-c(rep(2000,10))
SV.lmRatioM.model10.C5$Level<-c(rep(2000,10))

SM.lmRatioM.model10.C1<-melt(SM.lmRatioM.model10.C1, id.vars = "Level", measure.vars = method2)
SV.lmRatioM.model10.C1<-melt(SV.lmRatioM.model10.C1, id.vars = "Level", measure.vars = method2)
SM.lmRatioM.model10.C2<-melt(SM.lmRatioM.model10.C2, id.vars = "Level", measure.vars = method2)
SV.lmRatioM.model10.C2<-melt(SV.lmRatioM.model10.C2, id.vars = "Level", measure.vars = method2)
SM.lmRatioM.model10.C3<-melt(SM.lmRatioM.model10.C3, id.vars = "Level", measure.vars = method2)
SV.lmRatioM.model10.C3<-melt(SV.lmRatioM.model10.C3, id.vars = "Level", measure.vars = method2)
SM.lmRatioM.model10.C4<-melt(SM.lmRatioM.model10.C4, id.vars = "Level", measure.vars = method2)
SV.lmRatioM.model10.C4<-melt(SV.lmRatioM.model10.C4, id.vars = "Level", measure.vars = method2)
SM.lmRatioM.model10.C5<-melt(SM.lmRatioM.model10.C5, id.vars = "Level", measure.vars = method2)
SV.lmRatioM.model10.C5<-melt(SV.lmRatioM.model10.C5, id.vars = "Level", measure.vars = method2)

# merge datasets
SM.lmRatioM.model10CLevels<-do.call("rbind", list(SM.lmRatioM.model10.C1,SM.lmRatioM.model10.C2,SM.lmRatioM.model10.C3,SM.lmRatioM.model10.C4, SM.lmRatioM.model10.C5))
SV.lmRatioM.model10CLevels<-do.call("rbind", list(SV.lmRatioM.model10.C1,SV.lmRatioM.model10.C2,SV.lmRatioM.model10.C3,SV.lmRatioM.model10.C4, SV.lmRatioM.model10.C5))


# summarize for plotting
SM.lmRatioM.model10C.p<-data_summary(SM.lmRatioM.model10CLevels, varname="value", groupnames=c("Level", "variable"))
SV.lmRatioM.model10C.p<-data_summary(SV.lmRatioM.model10CLevels, varname="value", groupnames=c("Level", "variable"))
SM.lmRatioM.model10C.p2<-data_summary2(SM.lmRatioM.model10CLevels, varname="value", groupnames=c("Level", "variable"))
SV.lmRatioM.model10C.p2<-data_summary2(SV.lmRatioM.model10CLevels, varname="value", groupnames=c("Level", "variable"))
# plot
ggplot(SM.lmRatioM.model10C.p, aes(x=Level, y=value, group = variable, color=variable))+
  geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(30)) +
  scale_color_viridis_d(direction=-1)+
  geom_line(position=position_dodge(30))+
  geom_point(position=position_dodge(30))+
  xlab("Sequencing Depth")+
  ylab("Median lmRatio.model (Mean +/- sd)")+
  theme_classic()

ggplot(SV.lmRatioM.model10C.p, aes(x=Level, y=value, group = variable, color=variable))+
  geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(30)) +
  scale_color_viridis_d(direction=-1)+
  geom_line(position=position_dodge(30))+
  geom_point(position=position_dodge(30))+
  xlab("Sequencing Depth")+
  ylab("log Variance lmRatio.model (Mean +/- sd)")+
  theme_classic()

ggplot(SM.lmRatioM.model10C.p2, aes(x=Level, y=value, group = variable, color=variable))+
  geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(30)) +
  scale_color_viridis_d(direction=-1)+
  geom_line(position=position_dodge(30))+
  geom_point(position=position_dodge(30))+
  xlab("Sequencing Depth")+
  ylab("Median lmRatio.model (Median +/- min/max)")+
  theme_classic()

ggplot(SV.lmRatioM.model10C.p2, aes(x=Level, y=log(value), group = variable, color=variable))+
  geom_errorbar(aes(ymin=log(low), ymax=log(high)), width=.1, position=position_dodge(30)) +
  scale_color_viridis_d(direction=-1)+
  geom_line(position=position_dodge(30))+
  geom_point(position=position_dodge(30))+
  xlab("Sequencing Depth")+
  ylab("log Variance lmRatio.model (Median +/- min/max)")+
  theme_classic()

It is typical for the categorical model to have greater agreement across the methods than the environmental gradients.

summary(aov(SM.lmRatioM.model10CLevels$value~SM.lmRatioM.model10CLevels$Level*SM.lmRatioM.model10CLevels$variable))

##                                                                       Df
## SM.lmRatioM.model10CLevels$Level                                       1
## SM.lmRatioM.model10CLevels$variable                                    6
## SM.lmRatioM.model10CLevels$Level:SM.lmRatioM.model10CLevels$variable   6
## Residuals                                                            336
##                                                                       Sum Sq
## SM.lmRatioM.model10CLevels$Level                                     0.00521
## SM.lmRatioM.model10CLevels$variable                                  0.03459
## SM.lmRatioM.model10CLevels$Level:SM.lmRatioM.model10CLevels$variable 0.02608
## Residuals                                                            0.21403
##                                                                       Mean Sq
## SM.lmRatioM.model10CLevels$Level                                     0.005213
## SM.lmRatioM.model10CLevels$variable                                  0.005765
## SM.lmRatioM.model10CLevels$Level:SM.lmRatioM.model10CLevels$variable 0.004346
## Residuals                                                            0.000637
##                                                                      F value
## SM.lmRatioM.model10CLevels$Level                                       8.184
## SM.lmRatioM.model10CLevels$variable                                    9.050
## SM.lmRatioM.model10CLevels$Level:SM.lmRatioM.model10CLevels$variable   6.823
## Residuals                                                                   
##                                                                        Pr(>F)
## SM.lmRatioM.model10CLevels$Level                                      0.00449
## SM.lmRatioM.model10CLevels$variable                                  3.51e-09
## SM.lmRatioM.model10CLevels$Level:SM.lmRatioM.model10CLevels$variable 7.63e-07
## Residuals                                                                    
##                                                                         
## SM.lmRatioM.model10CLevels$Level                                     ** 
## SM.lmRatioM.model10CLevels$variable                                  ***
## SM.lmRatioM.model10CLevels$Level:SM.lmRatioM.model10CLevels$variable ***
## Residuals                                                               
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

TukeyHSD(aov(SM.lmRatioM.model10CLevels$value~SM.lmRatioM.model10CLevels$Level*SM.lmRatioM.model10CLevels$variable))

## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## SM.lmRatioM.model10CLevels$Level

## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## SM.lmRatioM.model10CLevels$Level, SM.lmRatioM.model10CLevels$variable

## Warning in TukeyHSD.aov(aov(SM.lmRatioM.model10CLevels$value ~
## SM.lmRatioM.model10CLevels$Level * : 'which' specified some non-factors which
## will be dropped

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = SM.lmRatioM.model10CLevels$value ~ SM.lmRatioM.model10CLevels$Level * SM.lmRatioM.model10CLevels$variable)
## 
## $`SM.lmRatioM.model10CLevels$variable`
##                          diff         lwr         upr     p adj
## QSeq0.5-raw     -2.874458e-02 -0.04371771 -0.01377145 0.0000006
## QSeq1-raw       -1.672331e-03 -0.01664546  0.01330080 0.9998931
## QSeq2-raw       -5.878274e-04 -0.01556096  0.01438530 0.9999998
## QSeq3-raw       -3.262371e-05 -0.01500575  0.01494051 1.0000000
## QSeq10-raw       2.109424e-15 -0.01497313  0.01497313 1.0000000
## QSeq100-raw      2.220446e-15 -0.01497313  0.01497313 1.0000000
## QSeq1-QSeq0.5    2.707225e-02  0.01209911  0.04204538 0.0000032
## QSeq2-QSeq0.5    2.815675e-02  0.01318362  0.04312988 0.0000010
## QSeq3-QSeq0.5    2.871195e-02  0.01373882  0.04368509 0.0000006
## QSeq10-QSeq0.5   2.874458e-02  0.01377145  0.04371771 0.0000006
## QSeq100-QSeq0.5  2.874458e-02  0.01377145  0.04371771 0.0000006
## QSeq2-QSeq1      1.084504e-03 -0.01388863  0.01605764 0.9999917
## QSeq3-QSeq1      1.639708e-03 -0.01333342  0.01661284 0.9999047
## QSeq10-QSeq1     1.672331e-03 -0.01330080  0.01664546 0.9998931
## QSeq100-QSeq1    1.672331e-03 -0.01330080  0.01664546 0.9998931
## QSeq3-QSeq2      5.552037e-04 -0.01441793  0.01552834 0.9999998
## QSeq10-QSeq2     5.878274e-04 -0.01438530  0.01556096 0.9999998
## QSeq100-QSeq2    5.878274e-04 -0.01438530  0.01556096 0.9999998
## QSeq10-QSeq3     3.262371e-05 -0.01494051  0.01500575 1.0000000
## QSeq100-QSeq3    3.262371e-05 -0.01494051  0.01500575 1.0000000
## QSeq100-QSeq10   1.110223e-16 -0.01497313  0.01497313 1.0000000

summary(aov(SV.lmRatioM.model10CLevels$value~SV.lmRatioM.model10CLevels$Level*SV.lmRatioM.model10CLevels$variable))

##                                                                       Df Sum Sq
## SV.lmRatioM.model10CLevels$Level                                       1 0.1757
## SV.lmRatioM.model10CLevels$variable                                    6 0.3277
## SV.lmRatioM.model10CLevels$Level:SV.lmRatioM.model10CLevels$variable   6 0.0292
## Residuals                                                            336 0.2823
##                                                                      Mean Sq
## SV.lmRatioM.model10CLevels$Level                                     0.17568
## SV.lmRatioM.model10CLevels$variable                                  0.05462
## SV.lmRatioM.model10CLevels$Level:SV.lmRatioM.model10CLevels$variable 0.00487
## Residuals                                                            0.00084
##                                                                      F value
## SV.lmRatioM.model10CLevels$Level                                     209.129
## SV.lmRatioM.model10CLevels$variable                                   65.018
## SV.lmRatioM.model10CLevels$Level:SV.lmRatioM.model10CLevels$variable   5.802
## Residuals                                                                   
##                                                                       Pr(>F)
## SV.lmRatioM.model10CLevels$Level                                     < 2e-16
## SV.lmRatioM.model10CLevels$variable                                  < 2e-16
## SV.lmRatioM.model10CLevels$Level:SV.lmRatioM.model10CLevels$variable 9.1e-06
## Residuals                                                                   
##                                                                         
## SV.lmRatioM.model10CLevels$Level                                     ***
## SV.lmRatioM.model10CLevels$variable                                  ***
## SV.lmRatioM.model10CLevels$Level:SV.lmRatioM.model10CLevels$variable ***
## Residuals                                                               
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

TukeyHSD(aov(SV.lmRatioM.model10CLevels$value~SV.lmRatioM.model10CLevels$Level*SV.lmRatioM.model10CLevels$variable))

## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## SV.lmRatioM.model10CLevels$Level

## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## SV.lmRatioM.model10CLevels$Level, SV.lmRatioM.model10CLevels$variable

## Warning in TukeyHSD.aov(aov(SV.lmRatioM.model10CLevels$value ~
## SV.lmRatioM.model10CLevels$Level * : 'which' specified some non-factors which
## will be dropped

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = SV.lmRatioM.model10CLevels$value ~ SV.lmRatioM.model10CLevels$Level * SV.lmRatioM.model10CLevels$variable)
## 
## $`SV.lmRatioM.model10CLevels$variable`
##                          diff         lwr          upr     p adj
## QSeq0.5-raw      0.0589309074  0.04173592  0.076125892 0.0000000
## QSeq1-raw        0.0057453442 -0.01144964  0.022940329 0.9557112
## QSeq2-raw       -0.0210906251 -0.03828561 -0.003895640 0.0058233
## QSeq3-raw       -0.0278245378 -0.04501952 -0.010629553 0.0000489
## QSeq10-raw      -0.0329843348 -0.05017932 -0.015789350 0.0000006
## QSeq100-raw     -0.0332472250 -0.05044221 -0.016052240 0.0000005
## QSeq1-QSeq0.5   -0.0531855633 -0.07038055 -0.035990578 0.0000000
## QSeq2-QSeq0.5   -0.0800215326 -0.09721652 -0.062826548 0.0000000
## QSeq3-QSeq0.5   -0.0867554452 -0.10395043 -0.069560460 0.0000000
## QSeq10-QSeq0.5  -0.0919152422 -0.10911023 -0.074720257 0.0000000
## QSeq100-QSeq0.5 -0.0921781324 -0.10937312 -0.074983148 0.0000000
## QSeq2-QSeq1     -0.0268359693 -0.04403095 -0.009640985 0.0001064
## QSeq3-QSeq1     -0.0335698820 -0.05076487 -0.016374897 0.0000003
## QSeq10-QSeq1    -0.0387296789 -0.05592466 -0.021534694 0.0000000
## QSeq100-QSeq1   -0.0389925691 -0.05618755 -0.021797584 0.0000000
## QSeq3-QSeq2     -0.0067339127 -0.02392890  0.010461072 0.9078826
## QSeq10-QSeq2    -0.0118937096 -0.02908869  0.005301275 0.3841698
## QSeq100-QSeq2   -0.0121565998 -0.02935158  0.005038385 0.3567277
## QSeq10-QSeq3    -0.0051597970 -0.02235478  0.012035188 0.9738926
## QSeq100-QSeq3   -0.0054226872 -0.02261767  0.011772298 0.9665702
## QSeq100-QSeq10  -0.0002628902 -0.01745787  0.016932095 1.0000000

Let’s look at the taxon relationships:

TaxRatio.model10.C1<-getTaxCor.Tab(model10.C1,method2)
TaxRatio.model10.C2<-getTaxCor.Tab(model10.C2,method2)
TaxRatio.model10.C3<-getTaxCor.Tab(model10.C3,method2)
TaxRatio.model10.C4<-getTaxCor.Tab(model10.C4,method2)
TaxRatio.model10.C5<-getTaxCor.Tab(model10.C5,method2)

V.TaxRatio.model10.C1<-melt(TaxRatio.model10.C1$V.tax)
M.TaxRatio.model10.C1<-melt(TaxRatio.model10.C1$Median.tax)
V.TaxRatio.model10.C2<-melt(TaxRatio.model10.C2$V.tax)
M.TaxRatio.model10.C2<-melt(TaxRatio.model10.C2$Median.tax)
V.TaxRatio.model10.C3<-melt(TaxRatio.model10.C3$V.tax)
M.TaxRatio.model10.C3<-melt(TaxRatio.model10.C3$Median.tax)
V.TaxRatio.model10.C4<-melt(TaxRatio.model10.C4$V.tax)
M.TaxRatio.model10.C4<-melt(TaxRatio.model10.C4$Median.tax)
V.TaxRatio.model10.C5<-melt(TaxRatio.model10.C5$V.tax)
M.TaxRatio.model10.C5<-melt(TaxRatio.model10.C5$Median.tax)

V.TaxRatio.model10.C1<-as.data.frame(V.TaxRatio.model10.C1)
M.TaxRatio.model10.C1<-as.data.frame(M.TaxRatio.model10.C1)
V.TaxRatio.model10.C2<-as.data.frame(V.TaxRatio.model10.C2)
M.TaxRatio.model10.C2<-as.data.frame(M.TaxRatio.model10.C2)
V.TaxRatio.model10.C3<-as.data.frame(V.TaxRatio.model10.C3)
M.TaxRatio.model10.C3<-as.data.frame(M.TaxRatio.model10.C3)
V.TaxRatio.model10.C4<-as.data.frame(V.TaxRatio.model10.C4)
M.TaxRatio.model10.C4<-as.data.frame(M.TaxRatio.model10.C4)
V.TaxRatio.model10.C5<-as.data.frame(V.TaxRatio.model10.C5)
M.TaxRatio.model10.C5<-as.data.frame(M.TaxRatio.model10.C5)

# prepare data for merging datasets

V.TaxRatio.model10.C1$Level<-c(rep(100,nrow(V.TaxRatio.model10.C1)))
V.TaxRatio.model10.C2$Level<-c(rep(200,nrow(V.TaxRatio.model10.C2)))
V.TaxRatio.model10.C3$Level<-c(rep(500,nrow(V.TaxRatio.model10.C3)))
V.TaxRatio.model10.C4$Level<-c(rep(1000,nrow(V.TaxRatio.model10.C4)))
V.TaxRatio.model10.C5$Level<-c(rep(2000,nrow(V.TaxRatio.model10.C5)))
M.TaxRatio.model10.C1$Level<-c(rep(100,nrow(M.TaxRatio.model10.C1)))
M.TaxRatio.model10.C2$Level<-c(rep(200,nrow(M.TaxRatio.model10.C2)))
M.TaxRatio.model10.C3$Level<-c(rep(500,nrow(M.TaxRatio.model10.C3)))
M.TaxRatio.model10.C4$Level<-c(rep(1000,nrow(M.TaxRatio.model10.C4)))
M.TaxRatio.model10.C5$Level<-c(rep(2000,nrow(M.TaxRatio.model10.C5)))


# merge datasets
V.TaxRatio.model10Levels<-do.call("rbind", list(V.TaxRatio.model10.C1,V.TaxRatio.model10.C2,V.TaxRatio.model10.C3,V.TaxRatio.model10.C4,V.TaxRatio.model10.C5))
M.TaxRatio.model10Levels<-do.call("rbind", list(M.TaxRatio.model10.C1,M.TaxRatio.model10.C2,M.TaxRatio.model10.C3,M.TaxRatio.model10.C4, M.TaxRatio.model10.C5))


# summarize for plotting
V.TaxRatio.model10.Seq.p<-data_summary(V.TaxRatio.model10Levels, varname="value", groupnames=c("Level", "Var2"))
M.TaxRatio.model10.Seq.p<-data_summary(M.TaxRatio.model10Levels, varname="value", groupnames=c("Level", "Var2"))
V.TaxRatio.model10.Seq.p2<-data_summary2(V.TaxRatio.model10Levels, varname="value", groupnames=c("Level", "Var2"))
M.TaxRatio.model10.Seq.p2<-data_summary2(M.TaxRatio.model10Levels, varname="value", groupnames=c("Level", "Var2"))
# plot
ggplot(V.TaxRatio.model10.Seq.p, aes(x=Level, y=value, group = Var2, color=Var2))+
  geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(100)) +
  scale_color_viridis_d(direction=-1)+
  geom_line(position=position_dodge(100))+
  geom_point(position=position_dodge(100))+
  xlab("Sequencing Depth")+
  ylab("Variance taxRatio (Mean +/- sd)")+
  theme_classic()

ggplot(M.TaxRatio.model10.Seq.p, aes(x=Level, y=value, group = Var2, color=Var2))+
  geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(100)) +
  scale_color_viridis_d(direction=-1)+
  geom_line(position=position_dodge(100))+
  geom_point(position=position_dodge(100))+
  xlab("Sequencing Depth")+
  ylab("Median taxRatio (Mean +/- sd)")+
  theme_classic()

ggplot(V.TaxRatio.model10.Seq.p2, aes(x=Level, y=log10(value), group = Var2, color=Var2))+
  geom_errorbar(aes(ymin=log10(low), ymax=log10(high)), width=.1, position=position_dodge(100)) +
  scale_color_viridis_d(direction=-1)+
  geom_line(position=position_dodge(100))+
  geom_point(position=position_dodge(100))+
  xlab("Sequencing Depth")+
  ylab("log10 Variance taxRatio (Median +/- min/max)")+
  theme_classic()

ggplot(M.TaxRatio.model10.Seq.p2, aes(x=Level, y=value, group = Var2, color=Var2))+
  geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(100)) +
  scale_color_viridis_d(direction=-1)+
  geom_line(position=position_dodge(100))+
  geom_point(position=position_dodge(100))+
  xlab("Sequencing Depth")+
  ylab("Median taxRatio (Median +/- min/max)")+
  theme_classic()

Remember that variance should approach zero and mean should approach 1 in a perfect world. Greater deviations from these values represent less accurate retention of taxon-taxon relationships.

summary(aov(M.TaxRatio.model10Levels$value~M.TaxRatio.model10Levels$Level*M.TaxRatio.model10Levels$Var2))

##                                                               Df Sum Sq Mean Sq
## M.TaxRatio.model10Levels$Level                                 1    0.3  0.2539
## M.TaxRatio.model10Levels$Var2                                  6    5.2  0.8629
## M.TaxRatio.model10Levels$Level:M.TaxRatio.model10Levels$Var2   6    4.7  0.7752
## Residuals                                                    336  319.5  0.9510
##                                                              F value Pr(>F)
## M.TaxRatio.model10Levels$Level                                 0.267  0.606
## M.TaxRatio.model10Levels$Var2                                  0.907  0.490
## M.TaxRatio.model10Levels$Level:M.TaxRatio.model10Levels$Var2   0.815  0.559
## Residuals

TukeyHSD(aov(M.TaxRatio.model10.Seq.p$value~M.TaxRatio.model10.Seq.p$Level*M.TaxRatio.model10.Seq.p$Var2))

## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## M.TaxRatio.model10.Seq.p$Level

## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## M.TaxRatio.model10.Seq.p$Level, M.TaxRatio.model10.Seq.p$Var2

## Warning in TukeyHSD.aov(aov(M.TaxRatio.model10.Seq.p$value ~
## M.TaxRatio.model10.Seq.p$Level * : 'which' specified some non-factors which will
## be dropped

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = M.TaxRatio.model10.Seq.p$value ~ M.TaxRatio.model10.Seq.p$Level * M.TaxRatio.model10.Seq.p$Var2)
## 
## $`M.TaxRatio.model10.Seq.p$Var2`
##                          diff        lwr       upr     p adj
## QSeq0.5-raw     -0.4385739507 -1.1206615 0.2435136 0.3931872
## QSeq1-raw       -0.2422962672 -0.9243838 0.4397913 0.9030558
## QSeq2-raw       -0.1721212384 -0.8542088 0.5099663 0.9800260
## QSeq3-raw       -0.1700517824 -0.8521394 0.5120358 0.9811991
## QSeq10-raw      -0.1563827393 -0.8384703 0.5257048 0.9877236
## QSeq100-raw     -0.1570590976 -0.8391467 0.5250285 0.9874477
## QSeq1-QSeq0.5    0.1962776835 -0.4858099 0.8783653 0.9621609
## QSeq2-QSeq0.5    0.2664527123 -0.4156349 0.9485403 0.8578009
## QSeq3-QSeq0.5    0.2685221683 -0.4135654 0.9506097 0.8534851
## QSeq10-QSeq0.5   0.2821912114 -0.3998964 0.9642788 0.8233586
## QSeq100-QSeq0.5  0.2815148531 -0.4005727 0.9636024 0.8249131
## QSeq2-QSeq1      0.0701750288 -0.6119125 0.7522626 0.9998579
## QSeq3-QSeq1      0.0722444848 -0.6098431 0.7543321 0.9998318
## QSeq10-QSeq1     0.0859135279 -0.5961741 0.7680011 0.9995427
## QSeq100-QSeq1    0.0852371696 -0.5968504 0.7673247 0.9995630
## QSeq3-QSeq2      0.0020694560 -0.6800181 0.6841570 1.0000000
## QSeq10-QSeq2     0.0157384991 -0.6663491 0.6978261 1.0000000
## QSeq100-QSeq2    0.0150621408 -0.6670254 0.6971497 1.0000000
## QSeq10-QSeq3     0.0136690431 -0.6684185 0.6957566 1.0000000
## QSeq100-QSeq3    0.0129926848 -0.6690949 0.6950803 1.0000000
## QSeq100-QSeq10  -0.0006763583 -0.6827639 0.6814112 1.0000000

summary(aov(V.TaxRatio.model10Levels$value~V.TaxRatio.model10Levels$Level*V.TaxRatio.model10Levels$Var2))

##                                                               Df    Sum Sq
## V.TaxRatio.model10Levels$Level                                 1 3.313e+08
## V.TaxRatio.model10Levels$Var2                                  6 7.557e+09
## V.TaxRatio.model10Levels$Level:V.TaxRatio.model10Levels$Var2   6 4.426e+09
## Residuals                                                    336 5.719e+11
##                                                                Mean Sq F value
## V.TaxRatio.model10Levels$Level                               3.313e+08   0.195
## V.TaxRatio.model10Levels$Var2                                1.259e+09   0.740
## V.TaxRatio.model10Levels$Level:V.TaxRatio.model10Levels$Var2 7.376e+08   0.433
## Residuals                                                    1.702e+09        
##                                                              Pr(>F)
## V.TaxRatio.model10Levels$Level                                0.659
## V.TaxRatio.model10Levels$Var2                                 0.618
## V.TaxRatio.model10Levels$Level:V.TaxRatio.model10Levels$Var2  0.856
## Residuals

TukeyHSD(aov(V.TaxRatio.model10Levels$value~V.TaxRatio.model10Levels$Level*V.TaxRatio.model10Levels$Var2))

## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## V.TaxRatio.model10Levels$Level

## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## V.TaxRatio.model10Levels$Level, V.TaxRatio.model10Levels$Var2

## Warning in TukeyHSD.aov(aov(V.TaxRatio.model10Levels$value ~
## V.TaxRatio.model10Levels$Level * : 'which' specified some non-factors which will
## be dropped

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = V.TaxRatio.model10Levels$value ~ V.TaxRatio.model10Levels$Level * V.TaxRatio.model10Levels$Var2)
## 
## $`V.TaxRatio.model10Levels$Var2`
##                         diff       lwr       upr     p adj
## QSeq0.5-raw     -14612.03415 -39088.42  9864.348 0.5687374
## QSeq1-raw       -13534.61986 -38011.00 10941.762 0.6562404
## QSeq2-raw       -12073.07256 -36549.45 12403.309 0.7664480
## QSeq3-raw       -12834.68642 -37311.07 11641.695 0.7107766
## QSeq10-raw      -12753.07522 -37229.46 11723.307 0.7169484
## QSeq100-raw     -12861.78757 -37338.17 11614.594 0.7087173
## QSeq1-QSeq0.5     1077.41429 -23398.97 25553.796 0.9999996
## QSeq2-QSeq0.5     2538.96159 -21937.42 27015.343 0.9999307
## QSeq3-QSeq0.5     1777.34773 -22699.03 26253.730 0.9999916
## QSeq10-QSeq0.5    1858.95893 -22617.42 26335.341 0.9999890
## QSeq100-QSeq0.5   1750.24658 -22726.14 26226.628 0.9999923
## QSeq2-QSeq1       1461.54731 -23014.83 25937.929 0.9999974
## QSeq3-QSeq1        699.93344 -23776.45 25176.315 1.0000000
## QSeq10-QSeq1       781.54465 -23694.84 25257.926 0.9999999
## QSeq100-QSeq1      672.83229 -23803.55 25149.214 1.0000000
## QSeq3-QSeq2       -761.61387 -25238.00 23714.768 0.9999999
## QSeq10-QSeq2      -680.00266 -25156.38 23796.379 1.0000000
## QSeq100-QSeq2     -788.71502 -25265.10 23687.667 0.9999999
## QSeq10-QSeq3        81.61121 -24394.77 24557.993 1.0000000
## QSeq100-QSeq3      -27.10115 -24503.48 24449.281 1.0000000
## QSeq100-QSeq10    -108.71236 -24585.09 24367.669 1.0000000

model10C1.Permanova.model<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1,method2, "CategoryRratio"))
model10C1.Permanova.env1<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1, method2, "F1Rratio"))
model10C1.Permanova.env2<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1, method2, "F2Rratio"))
model10C1.Permanova.env3<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1, method2, "F3Rratio"))
model10C1.Permanova.env4<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1, method2, "F4Rratio"))
model10C1.Permanova.env5<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1,method2, "F5Rratio"))


model10C2.Permanova.model<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C2, method2, "CategoryRratio"))
model10C2.Permanova.env1<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C2, method2, "F1Rratio"))
model10C2.Permanova.env2<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C2, method2, "F2Rratio"))
model10C2.Permanova.env3<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C2, method2, "F3Rratio"))
model10C2.Permanova.env4<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C2, method2, "F4Rratio"))
model10C2.Permanova.env5<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C2, method2, "F5Rratio"))


model10C3.Permanova.model<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C3, method2, "CategoryRratio"))
model10C3.Permanova.env1<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C3, method2, "F1Rratio"))
model10C3.Permanova.env2<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C3, method2, "F2Rratio"))
model10C3.Permanova.env3<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C3, method2, "F3Rratio"))
model10C3.Permanova.env4<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C3, method2, "F4Rratio"))
model10C3.Permanova.env5<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C3, method2, "F5Rratio"))


model10C4.Permanova.model<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C4, method2, "CategoryRratio"))
model10C4.Permanova.env1<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C4, method2, "F1Rratio"))
model10C4.Permanova.env2<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C4, method2, "F2Rratio"))
model10C4.Permanova.env3<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C4, method2, "F3Rratio"))
model10C4.Permanova.env4<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C4, method2, "F4Rratio"))
model10C4.Permanova.env5<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C4, method2, "F5Rratio"))

model10C5.Permanova.model<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C5, method2, "CategoryRratio"))
model10C5.Permanova.env1<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C5, method2, "F1Rratio"))
model10C5.Permanova.env2<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C5, method2, "F2Rratio"))
model10C5.Permanova.env3<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C5, method2, "F3Rratio"))
model10C5.Permanova.env4<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C5, method2, "F4Rratio"))
model10C5.Permanova.env5<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C5, method2, "F5Rratio"))

model10C1.Permanova.model$Level<-c(rep(100,10))
model10C1.Permanova.env1$Level<-c(rep(100,10))
model10C1.Permanova.env2$Level<-c(rep(100,10))
model10C1.Permanova.env3$Level<-c(rep(100,10))
model10C1.Permanova.env4$Level<-c(rep(100,10))
model10C1.Permanova.env5$Level<-c(rep(100,10))

model10C2.Permanova.model$Level<-c(rep(200,10))
model10C2.Permanova.env1$Level<-c(rep(200,10))
model10C2.Permanova.env2$Level<-c(rep(200,10))
model10C2.Permanova.env3$Level<-c(rep(200,10))
model10C2.Permanova.env4$Level<-c(rep(200,10))
model10C2.Permanova.env5$Level<-c(rep(200,10))

model10C3.Permanova.model$Level<-c(rep(500,10))
model10C3.Permanova.env1$Level<-c(rep(500,10))
model10C3.Permanova.env2$Level<-c(rep(500,10))
model10C3.Permanova.env3$Level<-c(rep(500,10))
model10C3.Permanova.env4$Level<-c(rep(500,10))
model10C3.Permanova.env5$Level<-c(rep(500,10))

model10C4.Permanova.model$Level<-c(rep(1000,10))
model10C4.Permanova.env1$Level<-c(rep(1000,10))
model10C4.Permanova.env2$Level<-c(rep(1000,10))
model10C4.Permanova.env3$Level<-c(rep(1000,10))
model10C4.Permanova.env4$Level<-c(rep(1000,10))
model10C4.Permanova.env5$Level<-c(rep(1000,10))

model10C5.Permanova.model$Level<-c(rep(2000,10))
model10C5.Permanova.env1$Level<-c(rep(2000,10))
model10C5.Permanova.env2$Level<-c(rep(2000,10))
model10C5.Permanova.env3$Level<-c(rep(2000,10))
model10C5.Permanova.env4$Level<-c(rep(2000,10))
model10C5.Permanova.env5$Level<-c(rep(2000,10))

permanova.model10CLevels.model<-do.call("rbind", list(model10C1.Permanova.model,model10C2.Permanova.model,model10C3.Permanova.model,model10C4.Permanova.model,model10C5.Permanova.model))
permanova.model10CLevels.env1<-do.call("rbind", list(model10C1.Permanova.env1,model10C2.Permanova.env1,model10C3.Permanova.env1,model10C4.Permanova.env1,model10C5.Permanova.env1))
permanova.model10CLevels.env2<-do.call("rbind", list(model10C1.Permanova.env2,model10C2.Permanova.env2,model10C3.Permanova.env2,model10C4.Permanova.env2,model10C5.Permanova.env2))
permanova.model10CLevels.env3<-do.call("rbind", list(model10C1.Permanova.env3,model10C2.Permanova.env3,model10C3.Permanova.env3,model10C4.Permanova.env3,model10C5.Permanova.env3))
permanova.model10CLevels.env4<-do.call("rbind", list(model10C1.Permanova.env4,model10C2.Permanova.env4,model10C3.Permanova.env4,model10C4.Permanova.env4,model10C5.Permanova.env4))
permanova.model10CLevels.env5<-do.call("rbind", list(model10C1.Permanova.env5,model10C2.Permanova.env5,model10C3.Permanova.env5,model10C4.Permanova.env5,model10C5.Permanova.env5))

permanova.model10CLevels.model<-melt(permanova.model10CLevels.model, id.vars = "Level", measure.vars = method2)
permanova.model10CLevels.env1<-melt(permanova.model10CLevels.env1, id.vars = "Level", measure.vars = method2)
permanova.model10CLevels.env2<-melt(permanova.model10CLevels.env2, id.vars = "Level", measure.vars = method2)
permanova.model10CLevels.env3<-melt(permanova.model10CLevels.env3, id.vars = "Level", measure.vars = method2)
permanova.model10CLevels.env4<-melt(permanova.model10CLevels.env4, id.vars = "Level", measure.vars = method2)
permanova.model10CLevels.env5<-melt(permanova.model10CLevels.env5, id.vars = "Level", measure.vars = method2)

permanova.model10CLevels.modelP<-data_summary2(permanova.model10CLevels.model, varname="value", groupnames=c("Level", "variable"))
permanova.model10CLevels.env1P<-data_summary2(permanova.model10CLevels.env1, varname="value", groupnames=c("Level", "variable"))
permanova.model10CLevels.env2P<-data_summary2(permanova.model10CLevels.env2, varname="value", groupnames=c("Level", "variable"))
permanova.model10CLevels.env3P<-data_summary2(permanova.model10CLevels.env3, varname="value", groupnames=c("Level", "variable"))
permanova.model10CLevels.env4P<-data_summary2(permanova.model10CLevels.env4, varname="value", groupnames=c("Level", "variable"))
permanova.model10CLevels.env5P<-data_summary2(permanova.model10CLevels.env5, varname="value", groupnames=c("Level", "variable"))


ggplot(permanova.model10CLevels.modelP, aes(x=Level, y=value, group = variable, color=variable))+
  geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(30)) +
  scale_colour_viridis_d(direction=-1)+
  geom_line(position=position_dodge(30))+
  geom_point(position=position_dodge(30))+
  xlab("Degree of Structure")+
  ylab("Permanova modelRatio (Median +/- min/max)")+
  theme_classic()

ggplot(permanova.model10CLevels.env1P, aes(x=Level, y=value, group = variable, color=variable))+
  geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(30)) +
  scale_colour_viridis_d(direction=-1)+
  geom_line(position=position_dodge(30))+
  geom_point(position=position_dodge(30))+
  xlab("Degree of Structure")+
  ylab("Permanova env1Ratio (Median +/- min/max)")+
  theme_classic()

ggplot(permanova.model10CLevels.env2P, aes(x=Level, y=value, group = variable, color=variable))+
  geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(30)) +
  scale_colour_viridis_d(direction=-1)+
  geom_line(position=position_dodge(30))+
  geom_point(position=position_dodge(30))+
  xlab("Degree of Structure")+
  ylab("Permanova env2Ratio (Median +/- min/max)")+
  theme_classic()

ggplot(permanova.model10CLevels.env3P, aes(x=Level, y=value, group = variable, color=variable))+
  geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(30)) +
  scale_colour_viridis_d(direction=-1)+
  geom_line(position=position_dodge(30))+
  geom_point(position=position_dodge(30))+
  xlab("Degree of Structure")+
  ylab("Permanova env3Ratio (Median +/- min/max)")+
  theme_classic()

ggplot(permanova.model10CLevels.env4P, aes(x=Level, y=value, group = variable, color=variable))+
  geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(30)) +
  scale_colour_viridis_d(direction=-1)+
  geom_line(position=position_dodge(30))+
  geom_point(position=position_dodge(30))+
  xlab("Degree of Structure")+
  ylab("Permanova env4Ratio (Median +/- min/max)")+
  theme_classic()

ggplot(permanova.model10CLevels.env5P, aes(x=Level, y=value, group = variable, color=variable))+
  geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(30)) +
  scale_colour_viridis_d(direction=-1)+
  geom_line(position=position_dodge(30))+
  geom_point(position=position_dodge(30))+
  xlab("Degree of Structure")+
  ylab("Permanova env5Ratio (Median +/- min/max)")+
  theme_classic()

Again, results are similar to the sparcity example where the experimental design is equally strongly detected across normalization methods, but that un-normalized data significantly underperforms in capturing the relationship between community structure and the environmental gradients.

summary(aov(permanova.model10CLevels.model$value~permanova.model10CLevels.model$Level*permanova.model10CLevels.model$variable))

##                                                                               Df
## permanova.model10CLevels.model$Level                                           1
## permanova.model10CLevels.model$variable                                        6
## permanova.model10CLevels.model$Level:permanova.model10CLevels.model$variable   6
## Residuals                                                                    336
##                                                                               Sum Sq
## permanova.model10CLevels.model$Level                                         0.08751
## permanova.model10CLevels.model$variable                                      0.00002
## permanova.model10CLevels.model$Level:permanova.model10CLevels.model$variable 0.00000
## Residuals                                                                    0.14051
##                                                                              Mean Sq
## permanova.model10CLevels.model$Level                                         0.08751
## permanova.model10CLevels.model$variable                                      0.00000
## permanova.model10CLevels.model$Level:permanova.model10CLevels.model$variable 0.00000
## Residuals                                                                    0.00042
##                                                                              F value
## permanova.model10CLevels.model$Level                                         209.260
## permanova.model10CLevels.model$variable                                        0.008
## permanova.model10CLevels.model$Level:permanova.model10CLevels.model$variable   0.001
## Residuals                                                                           
##                                                                              Pr(>F)
## permanova.model10CLevels.model$Level                                         <2e-16
## permanova.model10CLevels.model$variable                                           1
## permanova.model10CLevels.model$Level:permanova.model10CLevels.model$variable      1
## Residuals                                                                          
##                                                                                 
## permanova.model10CLevels.model$Level                                         ***
## permanova.model10CLevels.model$variable                                         
## permanova.model10CLevels.model$Level:permanova.model10CLevels.model$variable    
## Residuals                                                                       
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

TukeyHSD(aov(permanova.model10CLevels.model$value~permanova.model10CLevels.model$Level*permanova.model10CLevels.model$variable))

## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## permanova.model10CLevels.model$Level

## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## permanova.model10CLevels.model$Level, permanova.model10CLevels.model$variable

## Warning in TukeyHSD.aov(aov(permanova.model10CLevels.model$value ~
## permanova.model10CLevels.model$Level * : 'which' specified some non-factors
## which will be dropped

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = permanova.model10CLevels.model$value ~ permanova.model10CLevels.model$Level * permanova.model10CLevels.model$variable)
## 
## $`permanova.model10CLevels.model$variable`
##                          diff         lwr        upr     p adj
## QSeq0.5-raw     -7.208348e-04 -0.01285265 0.01141098 0.9999974
## QSeq1-raw       -7.543226e-06 -0.01213935 0.01212427 1.0000000
## QSeq2-raw       -1.117542e-04 -0.01224356 0.01202006 1.0000000
## QSeq3-raw       -8.359712e-05 -0.01221541 0.01204821 1.0000000
## QSeq10-raw      -1.663831e-05 -0.01214845 0.01211517 1.0000000
## QSeq100-raw     -2.220446e-16 -0.01213181 0.01213181 1.0000000
## QSeq1-QSeq0.5    7.132915e-04 -0.01141852 0.01284510 0.9999976
## QSeq2-QSeq0.5    6.090806e-04 -0.01152273 0.01274089 0.9999991
## QSeq3-QSeq0.5    6.372376e-04 -0.01149457 0.01276905 0.9999988
## QSeq10-QSeq0.5   7.041965e-04 -0.01142761 0.01283601 0.9999978
## QSeq100-QSeq0.5  7.208348e-04 -0.01141098 0.01285265 0.9999974
## QSeq2-QSeq1     -1.042110e-04 -0.01223602 0.01202760 1.0000000
## QSeq3-QSeq1     -7.605389e-05 -0.01220786 0.01205576 1.0000000
## QSeq10-QSeq1    -9.095080e-06 -0.01214091 0.01212272 1.0000000
## QSeq100-QSeq1    7.543226e-06 -0.01212427 0.01213935 1.0000000
## QSeq3-QSeq2      2.815707e-05 -0.01210365 0.01215997 1.0000000
## QSeq10-QSeq2     9.511588e-05 -0.01203669 0.01222693 1.0000000
## QSeq100-QSeq2    1.117542e-04 -0.01202006 0.01224356 1.0000000
## QSeq10-QSeq3     6.695881e-05 -0.01206485 0.01219877 1.0000000
## QSeq100-QSeq3    8.359712e-05 -0.01204821 0.01221541 1.0000000
## QSeq100-QSeq10   1.663831e-05 -0.01211517 0.01214845 1.0000000

summary(aov(permanova.model10CLevels.env1$value~permanova.model10CLevels.env1$Level*permanova.model10CLevels.env1$variable))

##                                                                             Df
## permanova.model10CLevels.env1$Level                                          1
## permanova.model10CLevels.env1$variable                                       6
## permanova.model10CLevels.env1$Level:permanova.model10CLevels.env1$variable   6
## Residuals                                                                  336
##                                                                            Sum Sq
## permanova.model10CLevels.env1$Level                                        0.0425
## permanova.model10CLevels.env1$variable                                     0.4600
## permanova.model10CLevels.env1$Level:permanova.model10CLevels.env1$variable 0.0864
## Residuals                                                                  1.1354
##                                                                            Mean Sq
## permanova.model10CLevels.env1$Level                                        0.04249
## permanova.model10CLevels.env1$variable                                     0.07667
## permanova.model10CLevels.env1$Level:permanova.model10CLevels.env1$variable 0.01439
## Residuals                                                                  0.00338
##                                                                            F value
## permanova.model10CLevels.env1$Level                                         12.574
## permanova.model10CLevels.env1$variable                                      22.689
## permanova.model10CLevels.env1$Level:permanova.model10CLevels.env1$variable   4.259
## Residuals                                                                         
##                                                                              Pr(>F)
## permanova.model10CLevels.env1$Level                                        0.000447
## permanova.model10CLevels.env1$variable                                      < 2e-16
## permanova.model10CLevels.env1$Level:permanova.model10CLevels.env1$variable 0.000376
## Residuals                                                                          
##                                                                               
## permanova.model10CLevels.env1$Level                                        ***
## permanova.model10CLevels.env1$variable                                     ***
## permanova.model10CLevels.env1$Level:permanova.model10CLevels.env1$variable ***
## Residuals                                                                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

TukeyHSD(aov(permanova.model10CLevels.env1$value~permanova.model10CLevels.env1$Level*permanova.model10CLevels.env1$variable))

## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## permanova.model10CLevels.env1$Level

## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## permanova.model10CLevels.env1$Level, permanova.model10CLevels.env1$variable

## Warning in TukeyHSD.aov(aov(permanova.model10CLevels.env1$value ~
## permanova.model10CLevels.env1$Level * : 'which' specified some non-factors which
## will be dropped

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = permanova.model10CLevels.env1$value ~ permanova.model10CLevels.env1$Level * permanova.model10CLevels.env1$variable)
## 
## $`permanova.model10CLevels.env1$variable`
##                         diff         lwr        upr p adj
## QSeq0.5-raw     1.030146e-01  0.06852811 0.13750101     0
## QSeq1-raw       1.032224e-01  0.06873592 0.13770882     0
## QSeq2-raw       1.037682e-01  0.06928172 0.13825462     0
## QSeq3-raw       1.038404e-01  0.06935391 0.13832681     0
## QSeq10-raw      1.038662e-01  0.06937978 0.13835268     0
## QSeq100-raw     1.038909e-01  0.06940448 0.13837739     0
## QSeq1-QSeq0.5   2.078109e-04 -0.03427864 0.03469426     1
## QSeq2-QSeq0.5   7.536109e-04 -0.03373284 0.03524006     1
## QSeq3-QSeq0.5   8.257986e-04 -0.03366065 0.03531225     1
## QSeq10-QSeq0.5  8.516714e-04 -0.03363478 0.03533812     1
## QSeq100-QSeq0.5 8.763743e-04 -0.03361008 0.03536283     1
## QSeq2-QSeq1     5.458000e-04 -0.03394065 0.03503225     1
## QSeq3-QSeq1     6.179877e-04 -0.03386847 0.03510444     1
## QSeq10-QSeq1    6.438605e-04 -0.03384259 0.03513031     1
## QSeq100-QSeq1   6.685634e-04 -0.03381789 0.03515502     1
## QSeq3-QSeq2     7.218769e-05 -0.03441427 0.03455864     1
## QSeq10-QSeq2    9.806049e-05 -0.03438839 0.03458451     1
## QSeq100-QSeq2   1.227634e-04 -0.03436369 0.03460922     1
## QSeq10-QSeq3    2.587280e-05 -0.03446058 0.03451233     1
## QSeq100-QSeq3   5.057568e-05 -0.03443588 0.03453703     1
## QSeq100-QSeq10  2.470288e-05 -0.03446175 0.03451116     1

summary(aov(permanova.model10CLevels.env2$value~permanova.model10CLevels.env2$Level*permanova.model10CLevels.env2$variable))

##                                                                             Df
## permanova.model10CLevels.env2$Level                                          1
## permanova.model10CLevels.env2$variable                                       6
## permanova.model10CLevels.env2$Level:permanova.model10CLevels.env2$variable   6
## Residuals                                                                  336
##                                                                            Sum Sq
## permanova.model10CLevels.env2$Level                                        0.1220
## permanova.model10CLevels.env2$variable                                     2.2082
## permanova.model10CLevels.env2$Level:permanova.model10CLevels.env2$variable 0.0007
## Residuals                                                                  1.8823
##                                                                            Mean Sq
## permanova.model10CLevels.env2$Level                                         0.1220
## permanova.model10CLevels.env2$variable                                      0.3680
## permanova.model10CLevels.env2$Level:permanova.model10CLevels.env2$variable  0.0001
## Residuals                                                                   0.0056
##                                                                            F value
## permanova.model10CLevels.env2$Level                                         21.777
## permanova.model10CLevels.env2$variable                                      65.698
## permanova.model10CLevels.env2$Level:permanova.model10CLevels.env2$variable   0.022
## Residuals                                                                         
##                                                                              Pr(>F)
## permanova.model10CLevels.env2$Level                                        4.43e-06
## permanova.model10CLevels.env2$variable                                      < 2e-16
## permanova.model10CLevels.env2$Level:permanova.model10CLevels.env2$variable        1
## Residuals                                                                          
##                                                                               
## permanova.model10CLevels.env2$Level                                        ***
## permanova.model10CLevels.env2$variable                                     ***
## permanova.model10CLevels.env2$Level:permanova.model10CLevels.env2$variable    
## Residuals                                                                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

TukeyHSD(aov(permanova.model10CLevels.env2$value~permanova.model10CLevels.env2$Level*permanova.model10CLevels.env2$variable))

## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## permanova.model10CLevels.env2$Level

## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## permanova.model10CLevels.env2$Level, permanova.model10CLevels.env2$variable

## Warning in TukeyHSD.aov(aov(permanova.model10CLevels.env2$value ~
## permanova.model10CLevels.env2$Level * : 'which' specified some non-factors which
## will be dropped

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = permanova.model10CLevels.env2$value ~ permanova.model10CLevels.env2$Level * permanova.model10CLevels.env2$variable)
## 
## $`permanova.model10CLevels.env2$variable`
##                          diff         lwr        upr p adj
## QSeq0.5-raw      2.266910e-01  0.18228744 0.27109456     0
## QSeq1-raw        2.265421e-01  0.18213854 0.27094566     0
## QSeq2-raw        2.271302e-01  0.18272661 0.27153372     0
## QSeq3-raw        2.272645e-01  0.18286094 0.27166806     0
## QSeq10-raw       2.271532e-01  0.18274965 0.27155677     0
## QSeq100-raw      2.271662e-01  0.18276268 0.27156980     0
## QSeq1-QSeq0.5   -1.489028e-04 -0.04455246 0.04425465     1
## QSeq2-QSeq0.5    4.391645e-04 -0.04396439 0.04484272     1
## QSeq3-QSeq0.5    5.734981e-04 -0.04383006 0.04497706     1
## QSeq10-QSeq0.5   4.622074e-04 -0.04394135 0.04486577     1
## QSeq100-QSeq0.5  4.752397e-04 -0.04392832 0.04487880     1
## QSeq2-QSeq1      5.880674e-04 -0.04381549 0.04499163     1
## QSeq3-QSeq1      7.224010e-04 -0.04368116 0.04512596     1
## QSeq10-QSeq1     6.111103e-04 -0.04379245 0.04501467     1
## QSeq100-QSeq1    6.241426e-04 -0.04377942 0.04502770     1
## QSeq3-QSeq2      1.343336e-04 -0.04426922 0.04453789     1
## QSeq10-QSeq2     2.304294e-05 -0.04438051 0.04442660     1
## QSeq100-QSeq2    3.607523e-05 -0.04436748 0.04443963     1
## QSeq10-QSeq3    -1.112907e-04 -0.04451485 0.04429227     1
## QSeq100-QSeq3   -9.825840e-05 -0.04450182 0.04430530     1
## QSeq100-QSeq10   1.303230e-05 -0.04439053 0.04441659     1

summary(aov(permanova.model10CLevels.env3$value~permanova.model10CLevels.env3$Level*permanova.model10CLevels.env3$variable))

##                                                                             Df
## permanova.model10CLevels.env3$Level                                          1
## permanova.model10CLevels.env3$variable                                       6
## permanova.model10CLevels.env3$Level:permanova.model10CLevels.env3$variable   6
## Residuals                                                                  336
##                                                                            Sum Sq
## permanova.model10CLevels.env3$Level                                        0.0771
## permanova.model10CLevels.env3$variable                                     1.0067
## permanova.model10CLevels.env3$Level:permanova.model10CLevels.env3$variable 0.0694
## Residuals                                                                  1.1620
##                                                                            Mean Sq
## permanova.model10CLevels.env3$Level                                        0.07705
## permanova.model10CLevels.env3$variable                                     0.16778
## permanova.model10CLevels.env3$Level:permanova.model10CLevels.env3$variable 0.01156
## Residuals                                                                  0.00346
##                                                                            F value
## permanova.model10CLevels.env3$Level                                         22.281
## permanova.model10CLevels.env3$variable                                      48.516
## permanova.model10CLevels.env3$Level:permanova.model10CLevels.env3$variable   3.343
## Residuals                                                                         
##                                                                              Pr(>F)
## permanova.model10CLevels.env3$Level                                        3.46e-06
## permanova.model10CLevels.env3$variable                                      < 2e-16
## permanova.model10CLevels.env3$Level:permanova.model10CLevels.env3$variable  0.00327
## Residuals                                                                          
##                                                                               
## permanova.model10CLevels.env3$Level                                        ***
## permanova.model10CLevels.env3$variable                                     ***
## permanova.model10CLevels.env3$Level:permanova.model10CLevels.env3$variable ** 
## Residuals                                                                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

TukeyHSD(aov(permanova.model10CLevels.env3$value~permanova.model10CLevels.env3$Level*permanova.model10CLevels.env3$variable))

## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## permanova.model10CLevels.env3$Level

## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## permanova.model10CLevels.env3$Level, permanova.model10CLevels.env3$variable

## Warning in TukeyHSD.aov(aov(permanova.model10CLevels.env3$value ~
## permanova.model10CLevels.env3$Level * : 'which' specified some non-factors which
## will be dropped

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = permanova.model10CLevels.env3$value ~ permanova.model10CLevels.env3$Level * permanova.model10CLevels.env3$variable)
## 
## $`permanova.model10CLevels.env3$variable`
##                          diff         lwr        upr p adj
## QSeq0.5-raw      1.534585e-01  0.11857061 0.18834645     0
## QSeq1-raw        1.534241e-01  0.11853622 0.18831206     0
## QSeq2-raw        1.528069e-01  0.11791902 0.18769486     0
## QSeq3-raw        1.530648e-01  0.11817684 0.18795267     0
## QSeq10-raw       1.533822e-01  0.11849430 0.18827014     0
## QSeq100-raw      1.534322e-01  0.11854428 0.18832012     0
## QSeq1-QSeq0.5   -3.439159e-05 -0.03492231 0.03485353     1
## QSeq2-QSeq0.5   -6.515900e-04 -0.03553951 0.03423633     1
## QSeq3-QSeq0.5   -3.937750e-04 -0.03528169 0.03449414     1
## QSeq10-QSeq0.5  -7.631251e-05 -0.03496423 0.03481161     1
## QSeq100-QSeq0.5 -2.632669e-05 -0.03491425 0.03486159     1
## QSeq2-QSeq1     -6.171984e-04 -0.03550512 0.03427072     1
## QSeq3-QSeq1     -3.593834e-04 -0.03524730 0.03452854     1
## QSeq10-QSeq1    -4.192093e-05 -0.03492984 0.03484600     1
## QSeq100-QSeq1    8.064893e-06 -0.03487985 0.03489598     1
## QSeq3-QSeq2      2.578150e-04 -0.03463010 0.03514573     1
## QSeq10-QSeq2     5.752775e-04 -0.03431264 0.03546320     1
## QSeq100-QSeq2    6.252633e-04 -0.03426266 0.03551318     1
## QSeq10-QSeq3     3.174625e-04 -0.03457046 0.03520538     1
## QSeq100-QSeq3    3.674483e-04 -0.03452047 0.03525537     1
## QSeq100-QSeq10   4.998582e-05 -0.03483793 0.03493790     1

summary(aov(permanova.model10CLevels.env4$value~permanova.model10CLevels.env4$Level*permanova.model10CLevels.env4$variable))

##                                                                             Df
## permanova.model10CLevels.env4$Level                                          1
## permanova.model10CLevels.env4$variable                                       6
## permanova.model10CLevels.env4$Level:permanova.model10CLevels.env4$variable   6
## Residuals                                                                  336
##                                                                            Sum Sq
## permanova.model10CLevels.env4$Level                                         0.080
## permanova.model10CLevels.env4$variable                                      0.358
## permanova.model10CLevels.env4$Level:permanova.model10CLevels.env4$variable  0.036
## Residuals                                                                   5.974
##                                                                            Mean Sq
## permanova.model10CLevels.env4$Level                                        0.08003
## permanova.model10CLevels.env4$variable                                     0.05962
## permanova.model10CLevels.env4$Level:permanova.model10CLevels.env4$variable 0.00602
## Residuals                                                                  0.01778
##                                                                            F value
## permanova.model10CLevels.env4$Level                                          4.501
## permanova.model10CLevels.env4$variable                                       3.354
## permanova.model10CLevels.env4$Level:permanova.model10CLevels.env4$variable   0.339
## Residuals                                                                         
##                                                                             Pr(>F)
## permanova.model10CLevels.env4$Level                                        0.03460
## permanova.model10CLevels.env4$variable                                     0.00319
## permanova.model10CLevels.env4$Level:permanova.model10CLevels.env4$variable 0.91619
## Residuals                                                                         
##                                                                              
## permanova.model10CLevels.env4$Level                                        * 
## permanova.model10CLevels.env4$variable                                     **
## permanova.model10CLevels.env4$Level:permanova.model10CLevels.env4$variable   
## Residuals                                                                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

TukeyHSD(aov(permanova.model10CLevels.env4$value~permanova.model10CLevels.env4$Level*permanova.model10CLevels.env4$variable))

## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## permanova.model10CLevels.env4$Level

## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## permanova.model10CLevels.env4$Level, permanova.model10CLevels.env4$variable

## Warning in TukeyHSD.aov(aov(permanova.model10CLevels.env4$value ~
## permanova.model10CLevels.env4$Level * : 'which' specified some non-factors which
## will be dropped

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = permanova.model10CLevels.env4$value ~ permanova.model10CLevels.env4$Level * permanova.model10CLevels.env4$variable)
## 
## $`permanova.model10CLevels.env4$variable`
##                          diff         lwr        upr     p adj
## QSeq0.5-raw      0.0920573542  0.01295399 0.17116072 0.0111039
## QSeq1-raw        0.0928939089  0.01379054 0.17199728 0.0099857
## QSeq2-raw        0.0895486165  0.01044525 0.16865198 0.0151694
## QSeq3-raw        0.0909219827  0.01181862 0.17002535 0.0128030
## QSeq10-raw       0.0913350074  0.01223164 0.17043838 0.0121595
## QSeq100-raw      0.0911812149  0.01207785 0.17028458 0.0123956
## QSeq1-QSeq0.5    0.0008365547 -0.07826681 0.07993992 1.0000000
## QSeq2-QSeq0.5   -0.0025087377 -0.08161211 0.07659463 0.9999999
## QSeq3-QSeq0.5   -0.0011353716 -0.08023874 0.07796800 1.0000000
## QSeq10-QSeq0.5  -0.0007223469 -0.07982571 0.07838102 1.0000000
## QSeq100-QSeq0.5 -0.0008761393 -0.07997951 0.07822723 1.0000000
## QSeq2-QSeq1     -0.0033452924 -0.08244866 0.07575808 0.9999997
## QSeq3-QSeq1     -0.0019719262 -0.08107529 0.07713144 1.0000000
## QSeq10-QSeq1    -0.0015589015 -0.08066227 0.07754447 1.0000000
## QSeq100-QSeq1   -0.0017126940 -0.08081606 0.07739067 1.0000000
## QSeq3-QSeq2      0.0013733661 -0.07773000 0.08047673 1.0000000
## QSeq10-QSeq2     0.0017863908 -0.07731698 0.08088976 1.0000000
## QSeq100-QSeq2    0.0016325984 -0.07747077 0.08073597 1.0000000
## QSeq10-QSeq3     0.0004130247 -0.07869034 0.07951639 1.0000000
## QSeq100-QSeq3    0.0002592323 -0.07884414 0.07936260 1.0000000
## QSeq100-QSeq10  -0.0001537924 -0.07925716 0.07894958 1.0000000

summary(aov(permanova.model10CLevels.env5$value~permanova.model10CLevels.env5$Level*permanova.model10CLevels.env5$variable))

##                                                                             Df
## permanova.model10CLevels.env5$Level                                          1
## permanova.model10CLevels.env5$variable                                       6
## permanova.model10CLevels.env5$Level:permanova.model10CLevels.env5$variable   6
## Residuals                                                                  336
##                                                                            Sum Sq
## permanova.model10CLevels.env5$Level                                         0.042
## permanova.model10CLevels.env5$variable                                      2.131
## permanova.model10CLevels.env5$Level:permanova.model10CLevels.env5$variable  0.027
## Residuals                                                                   4.465
##                                                                            Mean Sq
## permanova.model10CLevels.env5$Level                                         0.0424
## permanova.model10CLevels.env5$variable                                      0.3551
## permanova.model10CLevels.env5$Level:permanova.model10CLevels.env5$variable  0.0045
## Residuals                                                                   0.0133
##                                                                            F value
## permanova.model10CLevels.env5$Level                                          3.190
## permanova.model10CLevels.env5$variable                                      26.727
## permanova.model10CLevels.env5$Level:permanova.model10CLevels.env5$variable   0.342
## Residuals                                                                         
##                                                                            Pr(>F)
## permanova.model10CLevels.env5$Level                                         0.075
## permanova.model10CLevels.env5$variable                                     <2e-16
## permanova.model10CLevels.env5$Level:permanova.model10CLevels.env5$variable  0.915
## Residuals                                                                        
##                                                                               
## permanova.model10CLevels.env5$Level                                        .  
## permanova.model10CLevels.env5$variable                                     ***
## permanova.model10CLevels.env5$Level:permanova.model10CLevels.env5$variable    
## Residuals                                                                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

TukeyHSD(aov(permanova.model10CLevels.env5$value~permanova.model10CLevels.env5$Level*permanova.model10CLevels.env5$variable))

## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## permanova.model10CLevels.env5$Level

## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## permanova.model10CLevels.env5$Level, permanova.model10CLevels.env5$variable

## Warning in TukeyHSD.aov(aov(permanova.model10CLevels.env5$value ~
## permanova.model10CLevels.env5$Level * : 'which' specified some non-factors which
## will be dropped

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = permanova.model10CLevels.env5$value ~ permanova.model10CLevels.env5$Level * permanova.model10CLevels.env5$variable)
## 
## $`permanova.model10CLevels.env5$variable`
##                          diff         lwr        upr p adj
## QSeq0.5-raw      2.224973e-01  0.15411109 0.29088359     0
## QSeq1-raw        2.231785e-01  0.15479222 0.29156472     0
## QSeq2-raw        2.238929e-01  0.15550666 0.29227916     0
## QSeq3-raw        2.225283e-01  0.15414208 0.29091458     0
## QSeq10-raw       2.228817e-01  0.15449548 0.29126798     0
## QSeq100-raw      2.228581e-01  0.15447184 0.29124434     0
## QSeq1-QSeq0.5    6.811330e-04 -0.06770512 0.06906738     1
## QSeq2-QSeq0.5    1.395568e-03 -0.06699068 0.06978182     1
## QSeq3-QSeq0.5    3.098682e-05 -0.06835526 0.06841724     1
## QSeq10-QSeq0.5   3.843868e-04 -0.06800186 0.06877064     1
## QSeq100-QSeq0.5  3.607481e-04 -0.06802550 0.06874700     1
## QSeq2-QSeq1      7.144352e-04 -0.06767181 0.06910068     1
## QSeq3-QSeq1     -6.501462e-04 -0.06903640 0.06773610     1
## QSeq10-QSeq1    -2.967461e-04 -0.06868300 0.06808950     1
## QSeq100-QSeq1   -3.203849e-04 -0.06870663 0.06806586     1
## QSeq3-QSeq2     -1.364581e-03 -0.06975083 0.06702167     1
## QSeq10-QSeq2    -1.011181e-03 -0.06939743 0.06737507     1
## QSeq100-QSeq2   -1.034820e-03 -0.06942107 0.06735143     1
## QSeq10-QSeq3     3.534000e-04 -0.06803285 0.06873965     1
## QSeq100-QSeq3    3.297613e-04 -0.06805649 0.06871601     1
## QSeq100-QSeq10  -2.363877e-05 -0.06840989 0.06836261     1

leveneTest(permanova.model10CLevels.model$value~permanova.model10CLevels.model$variable)

## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value Pr(>F)
## group   6   0.001      1
##       343

leveneTest(permanova.model10CLevels.env1$value~permanova.model10CLevels.env1$variable)

## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value    Pr(>F)    
## group   6  17.336 < 2.2e-16 ***
##       343                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

leveneTest(permanova.model10CLevels.env2$value~permanova.model10CLevels.env2$variable)

## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value    Pr(>F)    
## group   6  28.579 < 2.2e-16 ***
##       343                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

leveneTest(permanova.model10CLevels.env3$value~permanova.model10CLevels.env3$variable)

## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value    Pr(>F)    
## group   6  18.108 < 2.2e-16 ***
##       343                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

leveneTest(permanova.model10CLevels.env4$value~permanova.model10CLevels.env4$variable)

## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value    Pr(>F)    
## group   6  19.103 < 2.2e-16 ***
##       343                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

leveneTest(permanova.model10CLevels.env5$value~permanova.model10CLevels.env5$variable)

## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value    Pr(>F)    
## group   6  33.051 < 2.2e-16 ***
##       343                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Expt 3: Normalization vs Sequencing Variance

By now you shuld be able to interpret the results; so I won’t explain everything (they are very consistent across experiments)

# sequencing variance ####
model10.C1V1<-BENCHMARK.MM(reps=10, commonN=20, groupN=20, singleN=15, D=500, V=50, method)

model10.C1V2<-BENCHMARK.MM(reps=10, commonN=20, groupN=20, singleN=15, D=500, V=100, method)

model10.C1V3<-BENCHMARK.MM(reps=10, commonN=20, groupN=20, singleN=15, D=500, V=250, method)

model10.C1V4<-BENCHMARK.MM(reps=10, commonN=20, groupN=20, singleN=15, D=500, V=500, method)

model10.C1V5<-BENCHMARK.MM(reps=10, commonN=20, groupN=20, singleN=15, D=500, V=1000, method)

LII output:

# sequencing variants LII ####

SummaryLII.model10.C1V1<-as.data.frame(Summarize.LII(model10.C1V1, method2)) # actually C3 ...
SummaryLII.model10.C1V2<-as.data.frame(Summarize.LII(model10.C1V2, method2)) 
SummaryLII.model10.C1V3<-as.data.frame(Summarize.LII(model10.C1V3, method2))
SummaryLII.model10.C1V4<-as.data.frame(Summarize.LII(model10.C1V4, method2))
SummaryLII.model10.C1V5<-as.data.frame(Summarize.LII(model10.C1V5, method2))
# prepare data for merging datasets
SummaryLII.model10.C1V1$Level<-c(rep(0.1,10))
SummaryLII.model10.C1V1<-melt(SummaryLII.model10.C1V1, id.vars = "Level", measure.vars = method2)
SummaryLII.model10.C1V2$Level<-c(rep(0.2,10))
SummaryLII.model10.C1V2<-melt(SummaryLII.model10.C1V2, id.vars = "Level", measure.vars = method2)
SummaryLII.model10.C1V3$Level<-c(rep(0.5,10))
SummaryLII.model10.C1V3<-melt(SummaryLII.model10.C1V3, id.vars = "Level", measure.vars = method2)
SummaryLII.model10.C1V4$Level<-c(rep(1,10))
SummaryLII.model10.C1V4<-melt(SummaryLII.model10.C1V4, id.vars = "Level", measure.vars = method2)
SummaryLII.model10.C1V5$Level<-c(rep(2,10))
SummaryLII.model10.C1V5<-melt(SummaryLII.model10.C1V5, id.vars = "Level", measure.vars = method2)
# merge datasets
model10.SeqVarLevels<-do.call("rbind", list(SummaryLII.model10.C1V1,SummaryLII.model10.C1V2,SummaryLII.model10.C1V3,SummaryLII.model10.C1V4,SummaryLII.model10.C1V5))

# summarize for plotting
model10.SeqVarLevels.summary<-data_summary(model10.SeqVarLevels, varname="value", groupnames=c("Level", "variable"))
model10.SeqVarLevels.summary2<-data_summary2(model10.SeqVarLevels, varname="value", groupnames=c("Level", "variable"))
# plot
ggplot(model10.SeqVarLevels.summary, aes(x=Level, y=value, group = variable, color=variable))+
  geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.1)) +
  scale_colour_viridis_d(direction=-1)+
  geom_line(position=position_dodge(.1))+
  geom_point(position=position_dodge(.1))+
  xlab("Sequencing Variance")+
  ylab("LII Value (Mean +/- sd)")+
  theme_classic()

ggplot(model10.SeqVarLevels.summary2, aes(x=Level, y=value, group = variable, color=variable))+
  geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(.1)) +
  scale_colour_viridis_d(direction=-1)+
  geom_line(position=position_dodge(.1))+
  geom_point(position=position_dodge(.1))+
  xlab("Sequencing Variance")+
  ylab("LII Value (Median +/- min/max)")+
  theme_classic()

summary(aov(SummaryLII.model10.C1V1$value~SummaryLII.model10.C1V1$Level*SummaryLII.model10.C1V1$variable))

##                                  Df  Sum Sq  Mean Sq F value   Pr(>F)    
## SummaryLII.model10.C1V1$variable  6 0.09284 0.015473    12.7 2.44e-09 ***
## Residuals                        63 0.07673 0.001218                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

TukeyHSD(aov(SummaryLII.model10.C1V1$value~SummaryLII.model10.C1V1$Level*SummaryLII.model10.C1V1$variable))

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = SummaryLII.model10.C1V1$value ~ SummaryLII.model10.C1V1$Level * SummaryLII.model10.C1V1$variable)
## 
## $`SummaryLII.model10.C1V1$variable`
##                          diff          lwr          upr     p adj
## QSeq0.5-raw      0.0521144723  0.004579925  0.099649020 0.0226951
## QSeq1-raw       -0.0157004439 -0.063234991  0.031834103 0.9508030
## QSeq2-raw       -0.0455986466 -0.093133194  0.001935901 0.0683197
## QSeq3-raw       -0.0489662830 -0.096500830 -0.001431736 0.0393541
## QSeq10-raw      -0.0535323011 -0.101066848 -0.005997754 0.0175333
## QSeq100-raw     -0.0537387272 -0.101273275 -0.006204180 0.0168783
## QSeq1-QSeq0.5   -0.0678149162 -0.115349464 -0.020280369 0.0009735
## QSeq2-QSeq0.5   -0.0977131189 -0.145247666 -0.050178571 0.0000008
## QSeq3-QSeq0.5   -0.1010807553 -0.148615303 -0.053546208 0.0000003
## QSeq10-QSeq0.5  -0.1056467734 -0.153181321 -0.058112226 0.0000001
## QSeq100-QSeq0.5 -0.1058531995 -0.153387747 -0.058318652 0.0000001
## QSeq2-QSeq1     -0.0298982027 -0.077432750  0.017636345 0.4779547
## QSeq3-QSeq1     -0.0332658390 -0.080800386  0.014268708 0.3475771
## QSeq10-QSeq1    -0.0378318572 -0.085366405  0.009702690 0.2060281
## QSeq100-QSeq1   -0.0380382833 -0.085572831  0.009496264 0.2007434
## QSeq3-QSeq2     -0.0033676364 -0.050902184  0.044166911 0.9999909
## QSeq10-QSeq2    -0.0079336545 -0.055468202  0.039600893 0.9986504
## QSeq100-QSeq2   -0.0081400806 -0.055674628  0.039394467 0.9984402
## QSeq10-QSeq3    -0.0045660181 -0.052100566  0.042968529 0.9999447
## QSeq100-QSeq3   -0.0047724442 -0.052306992  0.042762103 0.9999283
## QSeq100-QSeq10  -0.0002064261 -0.047740974  0.047328121 1.0000000

linear model outputs:

# sequencing variants lm ####

SM.lmRatio.model10.C1V1<-as.data.frame(Summarize.lmRatiotab.Median(model10.C1V1,method2))
SV.lmRatio.model10.C1V1<-as.data.frame(Summarize.lmRatiotab.Var(model10.C1V1,method2))
SM.lmRatio.model10.C1V2<-as.data.frame(Summarize.lmRatiotab.Median(model10.C1V2,method2))
SV.lmRatio.model10.C1V2<-as.data.frame(Summarize.lmRatiotab.Var(model10.C1V2,method2))
SM.lmRatio.model10.C1V3<-as.data.frame(Summarize.lmRatiotab.Median(model10.C1V3,method2))
SV.lmRatio.model10.C1V3<-as.data.frame(Summarize.lmRatiotab.Var(model10.C1V3,method2))
SM.lmRatio.model10.C1V4<-as.data.frame(Summarize.lmRatiotab.Median(model10.C1V4,method2))
SV.lmRatio.model10.C1V4<-as.data.frame(Summarize.lmRatiotab.Var(model10.C1V4,method2))
SM.lmRatio.model10.C1V5<-as.data.frame(Summarize.lmRatiotab.Median(model10.C1V5,method2))
SV.lmRatio.model10.C1V5<-as.data.frame(Summarize.lmRatiotab.Var(model10.C1V5,method2))
# prepare data for merging datasets

SM.lmRatio.model10.C1V1$Level<-c(rep(0.1,10))
SV.lmRatio.model10.C1V1$Level<-c(rep(0.1,10))
SM.lmRatio.model10.C1V2$Level<-c(rep(0.2,10))
SV.lmRatio.model10.C1V2$Level<-c(rep(0.2,10))
SM.lmRatio.model10.C1V3$Level<-c(rep(0.5,10))
SV.lmRatio.model10.C1V3$Level<-c(rep(0.5,10))
SM.lmRatio.model10.C1V4$Level<-c(rep(1,10))
SV.lmRatio.model10.C1V4$Level<-c(rep(1,10))
SM.lmRatio.model10.C1V5$Level<-c(rep(2,10))
SV.lmRatio.model10.C1V5$Level<-c(rep(2,10))

SM.lmRatio.model10.C1V1<-melt(SM.lmRatio.model10.C1V1, id.vars = "Level", measure.vars = method2)
SV.lmRatio.model10.C1V1<-melt(SV.lmRatio.model10.C1V1, id.vars = "Level", measure.vars = method2)
SM.lmRatio.model10.C1V2<-melt(SM.lmRatio.model10.C1V2, id.vars = "Level", measure.vars = method2)
SV.lmRatio.model10.C1V2<-melt(SV.lmRatio.model10.C1V2, id.vars = "Level", measure.vars = method2)
SM.lmRatio.model10.C1V3<-melt(SM.lmRatio.model10.C1V3, id.vars = "Level", measure.vars = method2)
SV.lmRatio.model10.C1V3<-melt(SV.lmRatio.model10.C1V3, id.vars = "Level", measure.vars = method2)
SM.lmRatio.model10.C1V4<-melt(SM.lmRatio.model10.C1V4, id.vars = "Level", measure.vars = method2)
SV.lmRatio.model10.C1V4<-melt(SV.lmRatio.model10.C1V4, id.vars = "Level", measure.vars = method2)
SM.lmRatio.model10.C1V5<-melt(SM.lmRatio.model10.C1V5, id.vars = "Level", measure.vars = method2)
SV.lmRatio.model10.C1V5<-melt(SV.lmRatio.model10.C1V5, id.vars = "Level", measure.vars = method2)

# merge datasets
SM.lmRatio.model10.CVLevels<-do.call("rbind", list(SM.lmRatio.model10.C1V1,SM.lmRatio.model10.C1V2,SM.lmRatio.model10.C1V3,SM.lmRatio.model10.C1V4, SM.lmRatio.model10.C1V5))
SV.lmRatio.model10.CVLevels<-do.call("rbind", list(SV.lmRatio.model10.C1V1,SV.lmRatio.model10.C1V2,SV.lmRatio.model10.C1V3,SV.lmRatio.model10.C1V4, SV.lmRatio.model10.C1V5))


# summarize for plotting
SM.lmRatio.model10CV.p<-data_summary(SM.lmRatio.model10.CVLevels, varname="value", groupnames=c("Level", "variable"))
SV.lmRatio.model10CV.p<-data_summary(SV.lmRatio.model10.CVLevels, varname="value", groupnames=c("Level", "variable"))
SM.lmRatio.model10CV.p2<-data_summary2(SM.lmRatio.model10.CVLevels, varname="value", groupnames=c("Level", "variable"))
SV.lmRatio.model10CV.p2<-data_summary2(SV.lmRatio.model10.CVLevels, varname="value", groupnames=c("Level", "variable"))
# plot
ggplot(SM.lmRatio.model10CV.p, aes(x=Level, y=value, group = variable, color=variable))+
  geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.01)) +
  scale_color_viridis_d(direction=-1)+
  geom_line(position=position_dodge(.01))+
  geom_point(position=position_dodge(.01))+
  xlab("Sequencing Variance")+
  ylab("Median lmRatio (Mean +/- sd)")+
  theme_classic()

## Warning: position_dodge requires non-overlapping x intervals

ggplot(SV.lmRatio.model10CV.p, aes(x=Level, y=value, group = variable, color=variable))+
  geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.01)) +
  scale_color_viridis_d(direction=-1)+
  geom_line(position=position_dodge(.01))+
  geom_point(position=position_dodge(.01))+
  xlab("Sequencing Variance")+
  ylab("Variance lmRatio (Mean +/- sd)")+
  theme_classic()

ggplot(SM.lmRatio.model10CV.p2, aes(x=Level, y=value, group = variable, color=variable))+
  geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(.01)) +
  scale_color_viridis_d(direction=-1)+
  geom_line(position=position_dodge(.01))+
  geom_point(position=position_dodge(.01))+
  xlab("Sequencing Variance")+
  ylab("Median lmRatio (Median +/- min/max)")+
  theme_classic()

## Warning: position_dodge requires non-overlapping x intervals

ggplot(SV.lmRatio.model10CV.p2, aes(x=Level, y=value, group = variable, color=variable))+
  geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(.01)) +
  scale_color_viridis_d(direction=-1)+
  geom_line(position=position_dodge(.01))+
  geom_point(position=position_dodge(.01))+
  xlab("Sequencing Variance")+
  ylab("Variance lmRatio (Median +/- min/max)")+
  theme_classic()

summary(aov(SM.lmRatio.model10.C1V1$value~SM.lmRatio.model10.C1V1$Level*SM.lmRatio.model10.C1V1$variable))

##                                  Df    Sum Sq   Mean Sq F value Pr(>F)
## SM.lmRatio.model10.C1V1$variable  6 0.0002424 4.040e-05   1.503  0.192
## Residuals                        63 0.0016933 2.688e-05

TukeyHSD(aov(SM.lmRatio.model10.C1V1$value~SM.lmRatio.model10.C1V1$Level*SM.lmRatio.model10.C1V1$variable))

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = SM.lmRatio.model10.C1V1$value ~ SM.lmRatio.model10.C1V1$Level * SM.lmRatio.model10.C1V1$variable)
## 
## $`SM.lmRatio.model10.C1V1$variable`
##                          diff          lwr         upr     p adj
## QSeq0.5-raw     -5.393265e-03 -0.012454510 0.001667980 0.2481258
## QSeq1-raw       -8.387205e-04 -0.007899966 0.006222525 0.9998085
## QSeq2-raw        1.110223e-16 -0.007061245 0.007061245 1.0000000
## QSeq3-raw        0.000000e+00 -0.007061245 0.007061245 1.0000000
## QSeq10-raw       0.000000e+00 -0.007061245 0.007061245 1.0000000
## QSeq100-raw      0.000000e+00 -0.007061245 0.007061245 1.0000000
## QSeq1-QSeq0.5    4.554544e-03 -0.002506701 0.011615790 0.4470462
## QSeq2-QSeq0.5    5.393265e-03 -0.001667980 0.012454510 0.2481258
## QSeq3-QSeq0.5    5.393265e-03 -0.001667980 0.012454510 0.2481258
## QSeq10-QSeq0.5   5.393265e-03 -0.001667980 0.012454510 0.2481258
## QSeq100-QSeq0.5  5.393265e-03 -0.001667980 0.012454510 0.2481258
## QSeq2-QSeq1      8.387205e-04 -0.006222525 0.007899966 0.9998085
## QSeq3-QSeq1      8.387205e-04 -0.006222525 0.007899966 0.9998085
## QSeq10-QSeq1     8.387205e-04 -0.006222525 0.007899966 0.9998085
## QSeq100-QSeq1    8.387205e-04 -0.006222525 0.007899966 0.9998085
## QSeq3-QSeq2     -1.110223e-16 -0.007061245 0.007061245 1.0000000
## QSeq10-QSeq2    -1.110223e-16 -0.007061245 0.007061245 1.0000000
## QSeq100-QSeq2   -1.110223e-16 -0.007061245 0.007061245 1.0000000
## QSeq10-QSeq3     0.000000e+00 -0.007061245 0.007061245 1.0000000
## QSeq100-QSeq3    0.000000e+00 -0.007061245 0.007061245 1.0000000
## QSeq100-QSeq10   0.000000e+00 -0.007061245 0.007061245 1.0000000

summary(aov(SV.lmRatio.model10.C1V1$value~SV.lmRatio.model10.C1V1$Level*SV.lmRatio.model10.C1V1$variable))

##                                  Df  Sum Sq  Mean Sq F value   Pr(>F)    
## SV.lmRatio.model10.C1V1$variable  6 0.04486 0.007476   5.711 8.65e-05 ***
## Residuals                        63 0.08248 0.001309                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

TukeyHSD(aov(SV.lmRatio.model10.C1V1$value~SV.lmRatio.model10.C1V1$Level*SV.lmRatio.model10.C1V1$variable))

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = SV.lmRatio.model10.C1V1$value ~ SV.lmRatio.model10.C1V1$Level * SV.lmRatio.model10.C1V1$variable)
## 
## $`SV.lmRatio.model10.C1V1$variable`
##                          diff          lwr          upr     p adj
## QSeq0.5-raw      4.579161e-02 -0.003489414  0.095072638 0.0852710
## QSeq1-raw        5.920835e-04 -0.048688942  0.049873109 1.0000000
## QSeq2-raw       -2.146596e-02 -0.070746987  0.027815065 0.8368936
## QSeq3-raw       -2.482717e-02 -0.074108198  0.024453854 0.7232841
## QSeq10-raw      -3.026851e-02 -0.079549535  0.019012516 0.5069458
## QSeq100-raw     -3.028966e-02 -0.079570687  0.018991365 0.5060983
## QSeq1-QSeq0.5   -4.519953e-02 -0.094480554  0.004081498 0.0929588
## QSeq2-QSeq0.5   -6.725757e-02 -0.116538598 -0.017976546 0.0018336
## QSeq3-QSeq0.5   -7.061878e-02 -0.119899810 -0.021337758 0.0009115
## QSeq10-QSeq0.5  -7.606012e-02 -0.125341147 -0.026779095 0.0002823
## QSeq100-QSeq0.5 -7.608127e-02 -0.125362299 -0.026800247 0.0002810
## QSeq2-QSeq1     -2.205804e-02 -0.071339070  0.027222982 0.8188536
## QSeq3-QSeq1     -2.541926e-02 -0.074700282  0.023861770 0.7009083
## QSeq10-QSeq1    -3.086059e-02 -0.080141619  0.018420433 0.4833416
## QSeq100-QSeq1   -3.088174e-02 -0.080162770  0.018399282 0.4825034
## QSeq3-QSeq2     -3.361211e-03 -0.052642237  0.045919814 0.9999927
## QSeq10-QSeq2    -8.802549e-03 -0.058083575  0.040478477 0.9980239
## QSeq100-QSeq2   -8.823700e-03 -0.058104726  0.040457326 0.9979972
## QSeq10-QSeq3    -5.441337e-03 -0.054722363  0.043839689 0.9998749
## QSeq100-QSeq3   -5.462489e-03 -0.054743515  0.043818537 0.9998720
## QSeq100-QSeq10  -2.115137e-05 -0.049302177  0.049259875 1.0000000

#sequence variants lm model ####
SM.lmRatio.model10.MC1V1<-as.data.frame(Summarize.lmRatiotabModel.Median(model10.C1V1,method2))
SV.lmRatio.model10.MC1V1<-as.data.frame(Summarize.lmRatiotabModel.Var(model10.C1V1,method2))
SM.lmRatio.model10.MC1V2<-as.data.frame(Summarize.lmRatiotabModel.Median(model10.C1V2,method2))
SV.lmRatio.model10.MC1V2<-as.data.frame(Summarize.lmRatiotabModel.Var(model10.C1V2,method2))
SM.lmRatio.model10.MC1V3<-as.data.frame(Summarize.lmRatiotabModel.Median(model10.C1V3,method2))
SV.lmRatio.model10.MC1V3<-as.data.frame(Summarize.lmRatiotabModel.Var(model10.C1V3,method2))
SM.lmRatio.model10.MC1V4<-as.data.frame(Summarize.lmRatiotabModel.Median(model10.C1V4,method2))
SV.lmRatio.model10.MC1V4<-as.data.frame(Summarize.lmRatiotabModel.Var(model10.C1V4,method2))
SM.lmRatio.model10.MC1V5<-as.data.frame(Summarize.lmRatiotabModel.Median(model10.C1V5,method2))
SV.lmRatio.model10.MC1V5<-as.data.frame(Summarize.lmRatiotabModel.Var(model10.C1V5,method2))
# prepare data for merging datasets

SM.lmRatio.model10.MC1V1$Level<-c(rep(0.1,10))
SV.lmRatio.model10.MC1V1$Level<-c(rep(0.1,10))
SM.lmRatio.model10.MC1V2$Level<-c(rep(0.2,10))
SV.lmRatio.model10.MC1V2$Level<-c(rep(0.2,10))
SM.lmRatio.model10.MC1V3$Level<-c(rep(0.5,10))
SV.lmRatio.model10.MC1V3$Level<-c(rep(0.5,10))
SM.lmRatio.model10.MC1V4$Level<-c(rep(1,10))
SV.lmRatio.model10.MC1V4$Level<-c(rep(1,10))
SM.lmRatio.model10.MC1V5$Level<-c(rep(2,10))
SV.lmRatio.model10.MC1V5$Level<-c(rep(2,10))

SM.lmRatio.model10.MC1V1<-melt(SM.lmRatio.model10.MC1V1, id.vars = "Level", measure.vars = method2)
SV.lmRatio.model10.MC1V1<-melt(SV.lmRatio.model10.MC1V1, id.vars = "Level", measure.vars = method2)
SM.lmRatio.model10.MC1V2<-melt(SM.lmRatio.model10.MC1V2, id.vars = "Level", measure.vars = method2)
SV.lmRatio.model10.MC1V2<-melt(SV.lmRatio.model10.MC1V2, id.vars = "Level", measure.vars = method2)
SM.lmRatio.model10.MC1V3<-melt(SM.lmRatio.model10.MC1V3, id.vars = "Level", measure.vars = method2)
SV.lmRatio.model10.MC1V3<-melt(SV.lmRatio.model10.MC1V3, id.vars = "Level", measure.vars = method2)
SM.lmRatio.model10.MC1V4<-melt(SM.lmRatio.model10.MC1V4, id.vars = "Level", measure.vars = method2)
SV.lmRatio.model10.MC1V4<-melt(SV.lmRatio.model10.MC1V4, id.vars = "Level", measure.vars = method2)
SM.lmRatio.model10.MC1V5<-melt(SM.lmRatio.model10.MC1V5, id.vars = "Level", measure.vars = method2)
SV.lmRatio.model10.MC1V5<-melt(SV.lmRatio.model10.MC1V5, id.vars = "Level", measure.vars = method2)

# merge datasets
SM.lmRatio.model10.MCVLevels<-do.call("rbind", list(SM.lmRatio.model10.MC1V1,SM.lmRatio.model10.MC1V2,SM.lmRatio.model10.MC1V3,SM.lmRatio.model10.MC1V4, SM.lmRatio.model10.MC1V5))
SV.lmRatio.model10.MCVLevels<-do.call("rbind", list(SV.lmRatio.model10.MC1V1,SV.lmRatio.model10.MC1V2,SV.lmRatio.model10.MC1V3,SV.lmRatio.model10.MC1V4, SV.lmRatio.model10.MC1V5))


# summarize for plotting
SM.lmRatio.model10MCV.p<-data_summary(SM.lmRatio.model10.MCVLevels, varname="value", groupnames=c("Level", "variable"))
SV.lmRatio.model10MCV.p<-data_summary(SV.lmRatio.model10.MCVLevels, varname="value", groupnames=c("Level", "variable"))

SM.lmRatio.model10MCV.p2<-data_summary2(SM.lmRatio.model10.MCVLevels, varname="value", groupnames=c("Level", "variable"))
SV.lmRatio.model10MCV.p2<-data_summary2(SV.lmRatio.model10.MCVLevels, varname="value", groupnames=c("Level", "variable"))
# plot
ggplot(SM.lmRatio.model10MCV.p, aes(x=Level, y=value, group = variable, color=variable))+
  geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.01)) +
  scale_color_viridis_d(direction=-1)+
  geom_line(position=position_dodge(.01))+
  geom_point(position=position_dodge(.01))+
  xlab("Sequencing Variance")+
  ylab("Median lmRatio (Mean +/- sd)")+
  theme_classic()

## Warning: position_dodge requires non-overlapping x intervals

ggplot(SV.lmRatio.model10MCV.p, aes(x=Level, y=value, group = variable, color=variable))+
  geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.01)) +
  scale_color_viridis_d(direction=-1)+
  geom_line(position=position_dodge(.01))+
  geom_point(position=position_dodge(.01))+
  xlab("Sequencing Variance")+
  ylab("Variance lmRatio (Mean +/- sd)")+
  theme_classic()

ggplot(SM.lmRatio.model10MCV.p2, aes(x=Level, y=value, group = variable, color=variable))+
  geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(.01)) +
  scale_color_viridis_d(direction=-1)+
  geom_line(position=position_dodge(.01))+
  geom_point(position=position_dodge(.01))+
  xlab("Sequencing Variance")+
  ylab("Median lmRatio (Median +/- min/max)")+
  theme_classic()

## Warning: position_dodge requires non-overlapping x intervals

ggplot(SV.lmRatio.model10MCV.p2, aes(x=Level, y=value, group = variable, color=variable))+
  geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(.01)) +
  scale_color_viridis_d(direction=-1)+
  geom_line(position=position_dodge(.01))+
  geom_point(position=position_dodge(.01))+
  xlab("Sequencing Variance")+
  ylab("Variance lmRatio (Median +/- min/max)")+
  theme_classic()

summary(aov(SM.lmRatio.model10.MC1V1$value~SM.lmRatio.model10.MC1V1$Level*SM.lmRatio.model10.MC1V1$variable))

##                                   Df    Sum Sq   Mean Sq F value Pr(>F)
## SM.lmRatio.model10.MC1V1$variable  6 1.816e-07 3.026e-08       1  0.433
## Residuals                         63 1.906e-06 3.026e-08

TukeyHSD(aov(SM.lmRatio.model10.MC1V1$value~SM.lmRatio.model10.C1V1$Level*SM.lmRatio.model10.MC1V1$variable))

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = SM.lmRatio.model10.MC1V1$value ~ SM.lmRatio.model10.C1V1$Level * SM.lmRatio.model10.MC1V1$variable)
## 
## $`SM.lmRatio.model10.MC1V1$variable`
##                          diff           lwr          upr     p adj
## QSeq0.5-raw     -1.455364e-04 -3.824615e-04 9.138875e-05 0.5068085
## QSeq1-raw       -1.110223e-16 -2.369251e-04 2.369251e-04 1.0000000
## QSeq2-raw        0.000000e+00 -2.369251e-04 2.369251e-04 1.0000000
## QSeq3-raw        0.000000e+00 -2.369251e-04 2.369251e-04 1.0000000
## QSeq10-raw       0.000000e+00 -2.369251e-04 2.369251e-04 1.0000000
## QSeq100-raw     -1.110223e-16 -2.369251e-04 2.369251e-04 1.0000000
## QSeq1-QSeq0.5    1.455364e-04 -9.138875e-05 3.824615e-04 0.5068085
## QSeq2-QSeq0.5    1.455364e-04 -9.138875e-05 3.824615e-04 0.5068085
## QSeq3-QSeq0.5    1.455364e-04 -9.138875e-05 3.824615e-04 0.5068085
## QSeq10-QSeq0.5   1.455364e-04 -9.138875e-05 3.824615e-04 0.5068085
## QSeq100-QSeq0.5  1.455364e-04 -9.138875e-05 3.824615e-04 0.5068085
## QSeq2-QSeq1      1.110223e-16 -2.369251e-04 2.369251e-04 1.0000000
## QSeq3-QSeq1      1.110223e-16 -2.369251e-04 2.369251e-04 1.0000000
## QSeq10-QSeq1     1.110223e-16 -2.369251e-04 2.369251e-04 1.0000000
## QSeq100-QSeq1    0.000000e+00 -2.369251e-04 2.369251e-04 1.0000000
## QSeq3-QSeq2      0.000000e+00 -2.369251e-04 2.369251e-04 1.0000000
## QSeq10-QSeq2     0.000000e+00 -2.369251e-04 2.369251e-04 1.0000000
## QSeq100-QSeq2   -1.110223e-16 -2.369251e-04 2.369251e-04 1.0000000
## QSeq10-QSeq3     0.000000e+00 -2.369251e-04 2.369251e-04 1.0000000
## QSeq100-QSeq3   -1.110223e-16 -2.369251e-04 2.369251e-04 1.0000000
## QSeq100-QSeq10  -1.110223e-16 -2.369251e-04 2.369251e-04 1.0000000

summary(aov(SV.lmRatio.model10.MC1V1$value~SV.lmRatio.model10.MC1V1$Level*SV.lmRatio.model10.MC1V1$variable))

##                                   Df  Sum Sq  Mean Sq F value   Pr(>F)    
## SV.lmRatio.model10.MC1V1$variable  6 0.06343 0.010572   14.55 2.45e-10 ***
## Residuals                         63 0.04578 0.000727                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

TukeyHSD(aov(SV.lmRatio.model10.MC1V1$value~SV.lmRatio.model10.MC1V1$Level*SV.lmRatio.model10.MC1V1$variable))

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = SV.lmRatio.model10.MC1V1$value ~ SV.lmRatio.model10.MC1V1$Level * SV.lmRatio.model10.MC1V1$variable)
## 
## $`SV.lmRatio.model10.MC1V1$variable`
##                          diff           lwr          upr     p adj
## QSeq0.5-raw      3.763425e-02  0.0009176365  0.074350857 0.0410116
## QSeq1-raw       -1.404508e-02 -0.0507616953  0.022671526 0.9044641
## QSeq2-raw       -4.013111e-02 -0.0768477220 -0.003414501 0.0233542
## QSeq3-raw       -4.348794e-02 -0.0802045477 -0.006771327 0.0104158
## QSeq10-raw      -4.890954e-02 -0.0856261517 -0.012192931 0.0025441
## QSeq100-raw     -4.897293e-02 -0.0856895437 -0.012256323 0.0025008
## QSeq1-QSeq0.5   -5.167933e-02 -0.0883959423 -0.014962721 0.0011861
## QSeq2-QSeq0.5   -7.776536e-02 -0.1144819690 -0.041048748 0.0000004
## QSeq3-QSeq0.5   -8.112218e-02 -0.1178387947 -0.044405574 0.0000001
## QSeq10-QSeq0.5  -8.654379e-02 -0.1232603987 -0.049827178 0.0000000
## QSeq100-QSeq0.5 -8.660718e-02 -0.1233237907 -0.049890570 0.0000000
## QSeq2-QSeq1     -2.608603e-02 -0.0628026372  0.010630584 0.3296626
## QSeq3-QSeq1     -2.944285e-02 -0.0661594628  0.007273758 0.1987363
## QSeq10-QSeq1    -3.486446e-02 -0.0715810669  0.001852154 0.0734536
## QSeq100-QSeq1   -3.492785e-02 -0.0716444589  0.001788762 0.0725184
## QSeq3-QSeq2     -3.356826e-03 -0.0400734361  0.033359785 0.9999587
## QSeq10-QSeq2    -8.778430e-03 -0.0454950402  0.027938181 0.9903017
## QSeq100-QSeq2   -8.841822e-03 -0.0455584321  0.027874789 0.9899258
## QSeq10-QSeq3    -5.421604e-03 -0.0421382145  0.031295006 0.9993273
## QSeq100-QSeq3   -5.484996e-03 -0.0422016065  0.031231614 0.9992811
## QSeq100-QSeq10  -6.339196e-05 -0.0367800024  0.036653219 1.0000000

Taxon correlation outputs:

# sequencing variants taxcor ####

TaxRatio.model10.C1V1<-getTaxCor.Tab(model10.C1V1,method2)
TaxRatio.model10.C1V2<-getTaxCor.Tab(model10.C1V2,method2)
TaxRatio.model10.C1V3<-getTaxCor.Tab(model10.C1V3,method2)
TaxRatio.model10.C1V4<-getTaxCor.Tab(model10.C1V4,method2)
TaxRatio.model10.C1V5<-getTaxCor.Tab(model10.C1V5,method2)

V.TaxRatio.model10.C1V1<-melt(TaxRatio.model10.C1V1$V.tax)
M.TaxRatio.model10.C1V1<-melt(TaxRatio.model10.C1V1$Median.tax)
V.TaxRatio.model10.C1V2<-melt(TaxRatio.model10.C1V2$V.tax)
M.TaxRatio.model10.C1V2<-melt(TaxRatio.model10.C1V2$Median.tax)
V.TaxRatio.model10.C1V3<-melt(TaxRatio.model10.C1V3$V.tax)
M.TaxRatio.model10.C1V3<-melt(TaxRatio.model10.C1V3$Median.tax)
V.TaxRatio.model10.C1V4<-melt(TaxRatio.model10.C1V4$V.tax)
M.TaxRatio.model10.C1V4<-melt(TaxRatio.model10.C1V4$Median.tax)
V.TaxRatio.model10.C1V5<-melt(TaxRatio.model10.C1V5$V.tax)
M.TaxRatio.model10.C1V5<-melt(TaxRatio.model10.C1V5$Median.tax)

V.TaxRatio.model10.C1V1<-as.data.frame(V.TaxRatio.model10.C1V1)
M.TaxRatio.model10.C1V1<-as.data.frame(M.TaxRatio.model10.C1V1)
V.TaxRatio.model10.C1V2<-as.data.frame(V.TaxRatio.model10.C1V2)
M.TaxRatio.model10.C1V2<-as.data.frame(M.TaxRatio.model10.C1V2)
V.TaxRatio.model10.C1V3<-as.data.frame(V.TaxRatio.model10.C1V3)
M.TaxRatio.model10.C1V3<-as.data.frame(M.TaxRatio.model10.C1V3)
V.TaxRatio.model10.C1V4<-as.data.frame(V.TaxRatio.model10.C1V4)
M.TaxRatio.model10.C1V4<-as.data.frame(M.TaxRatio.model10.C1V4)
V.TaxRatio.model10.C1V5<-as.data.frame(V.TaxRatio.model10.C1V5)
M.TaxRatio.model10.C1V5<-as.data.frame(M.TaxRatio.model10.C1V5)

# prepare data for merging datasets

V.TaxRatio.model10.C1V1$Level<-c(rep(0.1,nrow(V.TaxRatio.model10.C1V1)))
V.TaxRatio.model10.C1V2$Level<-c(rep(0.2,nrow(V.TaxRatio.model10.C1V2)))
V.TaxRatio.model10.C1V3$Level<-c(rep(0.5,nrow(V.TaxRatio.model10.C1V3)))
V.TaxRatio.model10.C1V4$Level<-c(rep(1,nrow(V.TaxRatio.model10.C1V4)))
V.TaxRatio.model10.C1V5$Level<-c(rep(2,nrow(V.TaxRatio.model10.C1V5)))
M.TaxRatio.model10.C1V1$Level<-c(rep(0.1,nrow(M.TaxRatio.model10.C1V1)))
M.TaxRatio.model10.C1V2$Level<-c(rep(0.2,nrow(M.TaxRatio.model10.C1V2)))
M.TaxRatio.model10.C1V3$Level<-c(rep(0.5,nrow(M.TaxRatio.model10.C1V3)))
M.TaxRatio.model10.C1V4$Level<-c(rep(1,nrow(M.TaxRatio.model10.C1V4)))
M.TaxRatio.model10.C1V5$Level<-c(rep(2,nrow(M.TaxRatio.model10.C1V5)))


# merge datasets
V.TaxRatio.model10VLevels<-do.call("rbind", list(V.TaxRatio.model10.C1V1,V.TaxRatio.model10.C1V2,V.TaxRatio.model10.C1V3,V.TaxRatio.model10.C1V4,V.TaxRatio.model10.C1V5))
M.TaxRatio.model10VLevels<-do.call("rbind", list(M.TaxRatio.model10.C1V1,M.TaxRatio.model10.C1V2,M.TaxRatio.model10.C1V3,M.TaxRatio.model10.C1V4, M.TaxRatio.model10.C1V5))


# summarize for plotting
V.TaxRatio.model10.SeqV.p<-data_summary(V.TaxRatio.model10VLevels, varname="value", groupnames=c("Level", "Var2"))
M.TaxRatio.model10.SeqV.p<-data_summary(M.TaxRatio.model10VLevels, varname="value", groupnames=c("Level", "Var2"))
# plot

V.TaxRatio.model10.SeqV.p2<-data_summary2(V.TaxRatio.model10VLevels, varname="value", groupnames=c("Level", "Var2"))
M.TaxRatio.model10.SeqV.p2<-data_summary2(M.TaxRatio.model10VLevels, varname="value", groupnames=c("Level", "Var2"))
# plot
ggplot(V.TaxRatio.model10.SeqV.p, aes(x=Level, y=value, group = Var2, color=Var2))+
  geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(0.1)) +
  scale_color_viridis_d(direction=-1)+
  geom_line(position=position_dodge(0.1))+
  geom_point(position=position_dodge(0.1))+
  xlab("Sequencing Depth")+
  ylab("log10 Variance taxRatio (Mean +/- sd)")+
  theme_classic()

## Warning in has_flipped_aes(data): probable complete loss of accuracy in modulus

## Warning in has_flipped_aes(data): probable complete loss of accuracy in modulus

## Warning in has_flipped_aes(data): probable complete loss of accuracy in modulus

## Warning in has_flipped_aes(data): probable complete loss of accuracy in modulus

## Warning in has_flipped_aes(data): probable complete loss of accuracy in modulus

## Warning in has_flipped_aes(data): probable complete loss of accuracy in modulus

## Warning in has_flipped_aes(data): probable complete loss of accuracy in modulus

ggplot(M.TaxRatio.model10.SeqV.p, aes(x=Level, y=value, group = Var2, color=Var2))+
  geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(0.1)) +
  scale_color_viridis_d(direction=-1)+
  geom_line(position=position_dodge(0.1))+
  geom_point(position=position_dodge(0.1))+
  xlab("Sequencing Depth")+
  ylab("Median taxRatio (Mean +/- sd)")+
  theme_classic()

ggplot(V.TaxRatio.model10.SeqV.p2, aes(x=Level, y=value, group = Var2, color=Var2))+
  geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(0.1)) +
  scale_color_viridis_d(direction=-1)+
  geom_line(position=position_dodge(0.1))+
  geom_point(position=position_dodge(0.1))+
  xlab("Sequencing Depth")+
  ylab("log10 Variance taxRatio (Median +/- min/max)")+
  theme_classic()

ggplot(M.TaxRatio.model10.SeqV.p2, aes(x=Level, y=value, group = Var2, color=Var2))+
  geom_errorbar(aes(ymin=low, ymax=high), width=.1, position=position_dodge(0.1)) +
  scale_color_viridis_d(direction=-1)+
  geom_line(position=position_dodge(0.1))+
  geom_point(position=position_dodge(0.1))+
  xlab("Sequencing Depth")+
  ylab("Median taxRatio (Median +/- min/max)")+
  theme_classic()

summary(aov(V.TaxRatio.model10VLevels$value~V.TaxRatio.model10VLevels$Level*V.TaxRatio.model10VLevels$Var2))

##                                                                 Df    Sum Sq
## V.TaxRatio.model10VLevels$Level                                  1 8.117e+69
## V.TaxRatio.model10VLevels$Var2                                   6 2.040e+69
## V.TaxRatio.model10VLevels$Level:V.TaxRatio.model10VLevels$Var2   6 1.842e+69
## Residuals                                                      336 5.304e+71
##                                                                  Mean Sq
## V.TaxRatio.model10VLevels$Level                                8.117e+69
## V.TaxRatio.model10VLevels$Var2                                 3.400e+68
## V.TaxRatio.model10VLevels$Level:V.TaxRatio.model10VLevels$Var2 3.070e+68
## Residuals                                                      1.579e+69
##                                                                F value Pr(>F)  
## V.TaxRatio.model10VLevels$Level                                  5.141  0.024 *
## V.TaxRatio.model10VLevels$Var2                                   0.215  0.972  
## V.TaxRatio.model10VLevels$Level:V.TaxRatio.model10VLevels$Var2   0.194  0.978  
## Residuals                                                                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

TukeyHSD(aov(V.TaxRatio.model10VLevels$value~V.TaxRatio.model10VLevels$Level*V.TaxRatio.model10VLevels$Var2))

## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## V.TaxRatio.model10VLevels$Level

## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## V.TaxRatio.model10VLevels$Level, V.TaxRatio.model10VLevels$Var2

## Warning in TukeyHSD.aov(aov(V.TaxRatio.model10VLevels$value ~
## V.TaxRatio.model10VLevels$Level * : 'which' specified some non-factors which
## will be dropped

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = V.TaxRatio.model10VLevels$value ~ V.TaxRatio.model10VLevels$Level * V.TaxRatio.model10VLevels$Var2)
## 
## $`V.TaxRatio.model10VLevels$Var2`
##                          diff           lwr          upr     p adj
## QSeq0.5-raw     -1.337561e+33 -2.490917e+34 2.223405e+34 0.9999981
## QSeq1-raw       -7.886313e+33 -3.145792e+34 1.568530e+34 0.9554309
## QSeq2-raw       -3.509279e+33 -2.708089e+34 2.006233e+34 0.9994324
## QSeq3-raw       -5.210814e+33 -2.878242e+34 1.836080e+34 0.9947651
## QSeq10-raw      -4.570373e+33 -2.814198e+34 1.900124e+34 0.9974613
## QSeq100-raw     -4.798541e+33 -2.837015e+34 1.877307e+34 0.9966721
## QSeq1-QSeq0.5   -6.548752e+33 -3.012036e+34 1.702286e+34 0.9823619
## QSeq2-QSeq0.5   -2.171719e+33 -2.574333e+34 2.139989e+34 0.9999655
## QSeq3-QSeq0.5   -3.873253e+33 -2.744486e+34 1.969836e+34 0.9990016
## QSeq10-QSeq0.5  -3.232813e+33 -2.680442e+34 2.033880e+34 0.9996464
## QSeq100-QSeq0.5 -3.460980e+33 -2.703259e+34 2.011063e+34 0.9994759
## QSeq2-QSeq1      4.377034e+33 -1.919458e+34 2.794864e+34 0.9980067
## QSeq3-QSeq1      2.675499e+33 -2.089611e+34 2.624711e+34 0.9998825
## QSeq10-QSeq1     3.315939e+33 -2.025567e+34 2.688755e+34 0.9995905
## QSeq100-QSeq1    3.087772e+33 -2.048384e+34 2.665938e+34 0.9997290
## QSeq3-QSeq2     -1.701535e+33 -2.527315e+34 2.187008e+34 0.9999919
## QSeq10-QSeq2    -1.061094e+33 -2.463270e+34 2.251052e+34 0.9999995
## QSeq100-QSeq2   -1.289261e+33 -2.486087e+34 2.228235e+34 0.9999984
## QSeq10-QSeq3     6.404407e+32 -2.293117e+34 2.421205e+34 1.0000000
## QSeq100-QSeq3    4.122734e+32 -2.315934e+34 2.398388e+34 1.0000000
## QSeq100-QSeq10  -2.281673e+32 -2.379978e+34 2.334344e+34 1.0000000

summary(aov(M.TaxRatio.model10VLevels$value~M.TaxRatio.model10VLevels$Level*M.TaxRatio.model10VLevels$Var2))

##                                                                 Df    Sum Sq
## M.TaxRatio.model10VLevels$Level                                  1 1.280e+30
## M.TaxRatio.model10VLevels$Var2                                   6 1.033e+29
## M.TaxRatio.model10VLevels$Level:M.TaxRatio.model10VLevels$Var2   6 9.327e+28
## Residuals                                                      336 7.314e+31
##                                                                  Mean Sq
## M.TaxRatio.model10VLevels$Level                                1.280e+30
## M.TaxRatio.model10VLevels$Var2                                 1.722e+28
## M.TaxRatio.model10VLevels$Level:M.TaxRatio.model10VLevels$Var2 1.555e+28
## Residuals                                                      2.177e+29
##                                                                F value Pr(>F)  
## M.TaxRatio.model10VLevels$Level                                  5.880 0.0158 *
## M.TaxRatio.model10VLevels$Var2                                   0.079 0.9981  
## M.TaxRatio.model10VLevels$Level:M.TaxRatio.model10VLevels$Var2   0.071 0.9986  
## Residuals                                                                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

TukeyHSD(aov(M.TaxRatio.model10VLevels$value~M.TaxRatio.model10VLevels$Var2))

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = M.TaxRatio.model10VLevels$value ~ M.TaxRatio.model10VLevels$Var2)
## 
## $`M.TaxRatio.model10VLevels$Var2`
##                          diff           lwr          upr     p adj
## QSeq0.5-raw     -6.802342e+12 -2.832820e+14 2.696773e+14 1.0000000
## QSeq1-raw       -5.721834e+13 -3.336980e+14 2.192613e+14 0.9963584
## QSeq2-raw       -1.927249e+13 -2.957522e+14 2.572072e+14 0.9999934
## QSeq3-raw       -3.092550e+13 -3.074052e+14 2.455542e+14 0.9998923
## QSeq10-raw      -2.627937e+13 -3.027590e+14 2.502003e+14 0.9999586
## QSeq100-raw     -2.789322e+13 -3.043729e+14 2.485864e+14 0.9999412
## QSeq1-QSeq0.5   -5.041599e+13 -3.268957e+14 2.260637e+14 0.9982018
## QSeq2-QSeq0.5   -1.247015e+13 -2.889498e+14 2.640095e+14 0.9999995
## QSeq3-QSeq0.5   -2.412315e+13 -3.006028e+14 2.523565e+14 0.9999750
## QSeq10-QSeq0.5  -1.947703e+13 -2.959567e+14 2.570026e+14 0.9999930
## QSeq100-QSeq0.5 -2.109088e+13 -2.975706e+14 2.553888e+14 0.9999887
## QSeq2-QSeq1      3.794585e+13 -2.385338e+14 3.144255e+14 0.9996453
## QSeq3-QSeq1      2.629284e+13 -2.501868e+14 3.027725e+14 0.9999585
## QSeq10-QSeq1     3.093896e+13 -2.455407e+14 3.074186e+14 0.9998920
## QSeq100-QSeq1    2.932511e+13 -2.471546e+14 3.058048e+14 0.9999211
## QSeq3-QSeq2     -1.165301e+13 -2.881327e+14 2.648267e+14 0.9999997
## QSeq10-QSeq2    -7.006886e+12 -2.834866e+14 2.694728e+14 1.0000000
## QSeq100-QSeq2   -8.620735e+12 -2.851004e+14 2.678589e+14 0.9999999
## QSeq10-QSeq3     4.646122e+12 -2.718335e+14 2.811258e+14 1.0000000
## QSeq100-QSeq3    3.032274e+12 -2.734474e+14 2.795119e+14 1.0000000
## QSeq100-QSeq10  -1.613848e+12 -2.780935e+14 2.748658e+14 1.0000000

PERMANOVA outputs:

# sequencing variants PERMANOVA ####

model10C1V1.Permanova.model<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V1,method2, "CategoryRratio"))
model10C1V1.Permanova.env1<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V1, method2, "F1Rratio"))
model10C1V1.Permanova.env2<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V1, method2, "F2Rratio"))
model10C1V1.Permanova.env3<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V1, method2, "F3Rratio"))
model10C1V1.Permanova.env4<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V1, method2, "F4Rratio"))
model10C1V1.Permanova.env5<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V1,method2, "F5Rratio"))


model10C1V2.Permanova.model<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V2, method2, "CategoryRratio"))
model10C1V2.Permanova.env1<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V2, method2, "F1Rratio"))
model10C1V2.Permanova.env2<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V2, method2, "F2Rratio"))
model10C1V2.Permanova.env3<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V2, method2, "F3Rratio"))
model10C1V2.Permanova.env4<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V2, method2, "F4Rratio"))
model10C1V2.Permanova.env5<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V2, method2, "F5Rratio"))


model10C1V3.Permanova.model<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V3, method2, "CategoryRratio"))
model10C1V3.Permanova.env1<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V3, method2, "F1Rratio"))
model10C1V3.Permanova.env2<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V3, method2, "F2Rratio"))
model10C1V3.Permanova.env3<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V3, method2, "F3Rratio"))
model10C1V3.Permanova.env4<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V3, method2, "F4Rratio"))
model10C1V3.Permanova.env5<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V3, method2, "F5Rratio"))


model10C1V4.Permanova.model<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V4, method2, "CategoryRratio"))
model10C1V4.Permanova.env1<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V4, method2, "F1Rratio"))
model10C1V4.Permanova.env2<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V4, method2, "F2Rratio"))
model10C1V4.Permanova.env3<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V4, method2, "F3Rratio"))
model10C1V4.Permanova.env4<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V4, method2, "F4Rratio"))
model10C1V4.Permanova.env5<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V4, method2, "F5Rratio"))

model10C1V5.Permanova.model<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V5, method2, "CategoryRratio"))
model10C1V5.Permanova.env1<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V5, method2, "F1Rratio"))
model10C1V5.Permanova.env2<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V5, method2, "F2Rratio"))
model10C1V5.Permanova.env3<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V5, method2, "F3Rratio"))
model10C1V5.Permanova.env4<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V5, method2, "F4Rratio"))
model10C1V5.Permanova.env5<-as.data.frame(Summarize.PERMANOVA.Rratio(model10.C1V5, method2, "F5Rratio"))

model10C1V1.Permanova.model$Level<-c(rep(0.1,10))
model10C1V1.Permanova.env1$Level<-c(rep(.100,10))
model10C1V1.Permanova.env2$Level<-c(rep(.100,10))
model10C1V1.Permanova.env3$Level<-c(rep(.100,10))
model10C1V1.Permanova.env4$Level<-c(rep(.100,10))
model10C1V1.Permanova.env5$Level<-c(rep(.100,10))

model10C1V2.Permanova.model$Level<-c(rep(.200,10))
model10C1V2.Permanova.env1$Level<-c(rep(.200,10))
model10C1V2.Permanova.env2$Level<-c(rep(.200,10))
model10C1V2.Permanova.env3$Level<-c(rep(.200,10))
model10C1V2.Permanova.env4$Level<-c(rep(.200,10))
model10C1V2.Permanova.env5$Level<-c(rep(.200,10))

model10C1V3.Permanova.model$Level<-c(rep(.500,10))
model10C1V3.Permanova.env1$Level<-c(rep(.500,10))
model10C1V3.Permanova.env2$Level<-c(rep(.500,10))
model10C1V3.Permanova.env3$Level<-c(rep(.500,10))
model10C1V3.Permanova.env4$Level<-c(rep(.500,10))
model10C1V3.Permanova.env5$Level<-c(rep(.500,10))

model10C1V4.Permanova.model$Level<-c(rep(1.000,10))
model10C1V4.Permanova.env1$Level<-c(rep(1.000,10))
model10C1V4.Permanova.env2$Level<-c(rep(1.000,10))
model10C1V4.Permanova.env3$Level<-c(rep(1.000,10))
model10C1V4.Permanova.env4$Level<-c(rep(1.000,10))
model10C1V4.Permanova.env5$Level<-c(rep(1.000,10))

model10C1V5.Permanova.model$Level<-c(rep(2.000,10))
model10C1V5.Permanova.env1$Level<-c(rep(2.000,10))
model10C1V5.Permanova.env2$Level<-c(rep(2.000,10))
model10C1V5.Permanova.env3$Level<-c(rep(2.000,10))
model10C1V5.Permanova.env4$Level<-c(rep(2.000,10))
model10C1V5.Permanova.env5$Level<-c(rep(2.000,10))

permanova.model10CVLevels.model<-do.call("rbind", list(model10C1V1.Permanova.model,model10C1V2.Permanova.model,model10C1V3.Permanova.model,model10C1V4.Permanova.model,model10C1V5.Permanova.model))
permanova.model10CVLevels.env1<-do.call("rbind", list(model10C1V1.Permanova.env1,model10C1V2.Permanova.env1,model10C1V3.Permanova.env1,model10C1V4.Permanova.env1,model10C1V5.Permanova.env1))
permanova.model10CVLevels.env2<-do.call("rbind", list(model10C1V1.Permanova.env2,model10C1V2.Permanova.env2,model10C1V3.Permanova.env2,model10C1V4.Permanova.env2,model10C1V5.Permanova.env2))
permanova.model10CVLevels.env3<-do.call("rbind", list(model10C1V1.Permanova.env3,model10C1V2.Permanova.env3,model10C1V3.Permanova.env3,model10C1V4.Permanova.env3,model10C1V5.Permanova.env3))
permanova.model10CVLevels.env4<-do.call("rbind", list(model10C1V1.Permanova.env4,model10C1V2.Permanova.env4,model10C1V3.Permanova.env4,model10C1V4.Permanova.env4,model10C1V5.Permanova.env4))
permanova.model10CVLevels.env5<-do.call("rbind", list(model10C1V1.Permanova.env5,model10C1V2.Permanova.env5,model10C1V3.Permanova.env5,model10C1V4.Permanova.env5,model10C1V5.Permanova.env5))

permanova.model10CVLevels.model<-melt(permanova.model10CVLevels.model, id.vars = "Level", measure.vars = method2)
permanova.model10CVLevels.env1<-melt(permanova.model10CVLevels.env1, id.vars = "Level", measure.vars = method2)
permanova.model10CVLevels.env2<-melt(permanova.model10CVLevels.env2, id.vars = "Level", measure.vars = method2)
permanova.model10CVLevels.env3<-melt(permanova.model10CVLevels.env3, id.vars = "Level", measure.vars = method2)
permanova.model10CVLevels.env4<-melt(permanova.model10CVLevels.env4, id.vars = "Level", measure.vars = method2)
permanova.model10CVLevels.env5<-melt(permanova.model10CVLevels.env5, id.vars = "Level", measure.vars = method2)

permanova.model10CVLevels.modelP<-data_summary(permanova.model10CVLevels.model, varname="value", groupnames=c("Level", "variable"))
permanova.model10CVLevels.env1P<-data_summary(permanova.model10CVLevels.env1, varname="value", groupnames=c("Level", "variable"))
permanova.model10CVLevels.env2P<-data_summary(permanova.model10CVLevels.env2, varname="value", groupnames=c("Level", "variable"))
permanova.model10CVLevels.env3P<-data_summary(permanova.model10CVLevels.env3, varname="value", groupnames=c("Level", "variable"))
permanova.model10CVLevels.env4P<-data_summary(permanova.model10CVLevels.env4, varname="value", groupnames=c("Level", "variable"))
permanova.model10CVLevels.env5P<-data_summary(permanova.model10CVLevels.env5, varname="value", groupnames=c("Level", "variable"))


ggplot(permanova.model10CVLevels.modelP, aes(x=Level, y=value, group = variable, color=variable))+
  geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.01)) +
  scale_colour_viridis_d(direction=-1)+
  geom_line(position=position_dodge(0.01))+
  geom_point(position=position_dodge(0.01))+
  xlab("Relative Variance (variance / mean)")+
  ylab("Permanova modelRatio (Mean +/- sd)")+
  theme_classic()

ggplot(permanova.model10CVLevels.env1P, aes(x=Level, y=value, group = variable, color=variable))+
  geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(0.1)) +
  scale_colour_viridis_d(direction=-1)+
  geom_line(position=position_dodge(0.1))+
  geom_point(position=position_dodge(0.1))+
  xlab("Relative Variance (variance / mean)")+
  ylab("Permanova env1Ratio (Mean +/- sd)")+
  theme_classic()

ggplot(permanova.model10CVLevels.env2P, aes(x=Level, y=value, group = variable, color=variable))+
  geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(0.1)) +
  scale_colour_viridis_d(direction=-1)+
  geom_line(position=position_dodge(0.1))+
  geom_point(position=position_dodge(0.1))+
  xlab("Relative Variance (variance / mean)")+
  ylab("Permanova env2Ratio (Mean +/- sd)")+
  theme_classic()

ggplot(permanova.model10CVLevels.env3P, aes(x=Level, y=value, group = variable, color=variable))+
  geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(0.1)) +
  scale_colour_viridis_d(direction=-1)+
  geom_line(position=position_dodge(0.1))+
  geom_point(position=position_dodge(0.1))+
  xlab("Relative Variance (variance / mean)")+
  ylab("Permanova env3Ratio (Mean +/- sd)")+
  theme_classic()

ggplot(permanova.model10CVLevels.env4P, aes(x=Level, y=value, group = variable, color=variable))+
  geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(0.1)) +
  scale_colour_viridis_d(direction=-1)+
  geom_line(position=position_dodge(0.1))+
  geom_point(position=position_dodge(0.1))+
  xlab("Relative Variance (variance / mean)")+
  ylab("Permanova env4Ratio (Mean +/- sd)")+
  theme_classic()

ggplot(permanova.model10CVLevels.env5P, aes(x=Level, y=value, group = variable, color=variable))+
  geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(0.1)) +
  scale_colour_viridis_d(direction=-1)+
  geom_line(position=position_dodge(0.1))+
  geom_point(position=position_dodge(0.1))+
  xlab("Relative Variance (variance / mean)")+
  ylab("Permanova env5Ratio (Mean +/- sd)")+
  theme_classic()

summary(aov(permanova.model10CVLevels.model$value~permanova.model10CVLevels.model$Level*permanova.model10CVLevels.model$variable))

##                                                                                 Df
## permanova.model10CVLevels.model$Level                                            1
## permanova.model10CVLevels.model$variable                                         6
## permanova.model10CVLevels.model$Level:permanova.model10CVLevels.model$variable   6
## Residuals                                                                      336
##                                                                                 Sum Sq
## permanova.model10CVLevels.model$Level                                          0.01517
## permanova.model10CVLevels.model$variable                                       0.00003
## permanova.model10CVLevels.model$Level:permanova.model10CVLevels.model$variable 0.00000
## Residuals                                                                      0.03802
##                                                                                 Mean Sq
## permanova.model10CVLevels.model$Level                                          0.015165
## permanova.model10CVLevels.model$variable                                       0.000004
## permanova.model10CVLevels.model$Level:permanova.model10CVLevels.model$variable 0.000000
## Residuals                                                                      0.000113
##                                                                                F value
## permanova.model10CVLevels.model$Level                                          134.017
## permanova.model10CVLevels.model$variable                                         0.039
## permanova.model10CVLevels.model$Level:permanova.model10CVLevels.model$variable   0.002
## Residuals                                                                             
##                                                                                Pr(>F)
## permanova.model10CVLevels.model$Level                                          <2e-16
## permanova.model10CVLevels.model$variable                                            1
## permanova.model10CVLevels.model$Level:permanova.model10CVLevels.model$variable      1
## Residuals                                                                            
##                                                                                   
## permanova.model10CVLevels.model$Level                                          ***
## permanova.model10CVLevels.model$variable                                          
## permanova.model10CVLevels.model$Level:permanova.model10CVLevels.model$variable    
## Residuals                                                                         
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

TukeyHSD(aov(permanova.model10CVLevels.model$value~permanova.model10CVLevels.model$Level*permanova.model10CVLevels.model$variable))

## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## permanova.model10CVLevels.model$Level

## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## permanova.model10CVLevels.model$Level, permanova.model10CVLevels.model$variable

## Warning in TukeyHSD.aov(aov(permanova.model10CVLevels.model$value ~
## permanova.model10CVLevels.model$Level * : 'which' specified some non-factors
## which will be dropped

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = permanova.model10CVLevels.model$value ~ permanova.model10CVLevels.model$Level * permanova.model10CVLevels.model$variable)
## 
## $`permanova.model10CVLevels.model$variable`
##                          diff          lwr         upr     p adj
## QSeq0.5-raw     -7.976089e-04 -0.007108458 0.005513241 0.9997799
## QSeq1-raw       -3.568511e-05 -0.006346535 0.006275164 1.0000000
## QSeq2-raw       -4.356960e-08 -0.006310893 0.006310806 1.0000000
## QSeq3-raw       -1.223197e-05 -0.006323081 0.006298617 1.0000000
## QSeq10-raw       2.607455e-06 -0.006308242 0.006313457 1.0000000
## QSeq100-raw      0.000000e+00 -0.006310849 0.006310849 1.0000000
## QSeq1-QSeq0.5    7.619238e-04 -0.005548926 0.007072773 0.9998314
## QSeq2-QSeq0.5    7.975653e-04 -0.005513284 0.007108415 0.9997800
## QSeq3-QSeq0.5    7.853769e-04 -0.005525473 0.007096226 0.9997989
## QSeq10-QSeq0.5   8.002163e-04 -0.005510633 0.007111066 0.9997757
## QSeq100-QSeq0.5  7.976089e-04 -0.005513241 0.007108458 0.9997799
## QSeq2-QSeq1      3.564154e-05 -0.006275208 0.006346491 1.0000000
## QSeq3-QSeq1      2.345315e-05 -0.006287396 0.006334303 1.0000000
## QSeq10-QSeq1     3.829257e-05 -0.006272557 0.006349142 1.0000000
## QSeq100-QSeq1    3.568511e-05 -0.006275164 0.006346535 1.0000000
## QSeq3-QSeq2     -1.218840e-05 -0.006323038 0.006298661 1.0000000
## QSeq10-QSeq2     2.651025e-06 -0.006308198 0.006313500 1.0000000
## QSeq100-QSeq2    4.356960e-08 -0.006310806 0.006310893 1.0000000
## QSeq10-QSeq3     1.483942e-05 -0.006296010 0.006325689 1.0000000
## QSeq100-QSeq3    1.223197e-05 -0.006298617 0.006323081 1.0000000
## QSeq100-QSeq10  -2.607455e-06 -0.006313457 0.006308242 1.0000000

summary(aov(permanova.model10CVLevels.env1$value~permanova.model10CVLevels.env1$Level*permanova.model10CVLevels.env1$variable))

##                                                                               Df
## permanova.model10CVLevels.env1$Level                                           1
## permanova.model10CVLevels.env1$variable                                        6
## permanova.model10CVLevels.env1$Level:permanova.model10CVLevels.env1$variable   6
## Residuals                                                                    336
##                                                                              Sum Sq
## permanova.model10CVLevels.env1$Level                                         0.1694
## permanova.model10CVLevels.env1$variable                                      0.3480
## permanova.model10CVLevels.env1$Level:permanova.model10CVLevels.env1$variable 0.4818
## Residuals                                                                    1.0218
##                                                                              Mean Sq
## permanova.model10CVLevels.env1$Level                                         0.16943
## permanova.model10CVLevels.env1$variable                                      0.05800
## permanova.model10CVLevels.env1$Level:permanova.model10CVLevels.env1$variable 0.08030
## Residuals                                                                    0.00304
##                                                                              F value
## permanova.model10CVLevels.env1$Level                                           55.71
## permanova.model10CVLevels.env1$variable                                        19.07
## permanova.model10CVLevels.env1$Level:permanova.model10CVLevels.env1$variable   26.40
## Residuals                                                                           
##                                                                                Pr(>F)
## permanova.model10CVLevels.env1$Level                                         7.26e-13
## permanova.model10CVLevels.env1$variable                                       < 2e-16
## permanova.model10CVLevels.env1$Level:permanova.model10CVLevels.env1$variable  < 2e-16
## Residuals                                                                            
##                                                                                 
## permanova.model10CVLevels.env1$Level                                         ***
## permanova.model10CVLevels.env1$variable                                      ***
## permanova.model10CVLevels.env1$Level:permanova.model10CVLevels.env1$variable ***
## Residuals                                                                       
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

TukeyHSD(aov(permanova.model10CVLevels.env1$value~permanova.model10CVLevels.env1$Level*permanova.model10CVLevels.env1$variable))

## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## permanova.model10CVLevels.env1$Level

## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## permanova.model10CVLevels.env1$Level, permanova.model10CVLevels.env1$variable

## Warning in TukeyHSD.aov(aov(permanova.model10CVLevels.env1$value ~
## permanova.model10CVLevels.env1$Level * : 'which' specified some non-factors
## which will be dropped

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = permanova.model10CVLevels.env1$value ~ permanova.model10CVLevels.env1$Level * permanova.model10CVLevels.env1$variable)
## 
## $`permanova.model10CVLevels.env1$variable`
##                          diff         lwr        upr     p adj
## QSeq0.5-raw      8.880173e-02  0.05608512 0.12151833 0.0000000
## QSeq1-raw        9.095665e-02  0.05824004 0.12367325 0.0000000
## QSeq2-raw        9.011607e-02  0.05739947 0.12283268 0.0000000
## QSeq3-raw        9.015091e-02  0.05743430 0.12286751 0.0000000
## QSeq10-raw       9.027340e-02  0.05755679 0.12299000 0.0000000
## QSeq100-raw      9.029021e-02  0.05757360 0.12300681 0.0000000
## QSeq1-QSeq0.5    2.154921e-03 -0.03056168 0.03487153 0.9999953
## QSeq2-QSeq0.5    1.314347e-03 -0.03140226 0.03403095 0.9999998
## QSeq3-QSeq0.5    1.349180e-03 -0.03136742 0.03406578 0.9999997
## QSeq10-QSeq0.5   1.471670e-03 -0.03124493 0.03418827 0.9999995
## QSeq100-QSeq0.5  1.488478e-03 -0.03122813 0.03420508 0.9999995
## QSeq2-QSeq1     -8.405745e-04 -0.03355718 0.03187603 1.0000000
## QSeq3-QSeq1     -8.057416e-04 -0.03352235 0.03191086 1.0000000
## QSeq10-QSeq1    -6.832510e-04 -0.03339986 0.03203335 1.0000000
## QSeq100-QSeq1   -6.664430e-04 -0.03338305 0.03205016 1.0000000
## QSeq3-QSeq2      3.483288e-05 -0.03268177 0.03275144 1.0000000
## QSeq10-QSeq2     1.573235e-04 -0.03255928 0.03287393 1.0000000
## QSeq100-QSeq2    1.741315e-04 -0.03254247 0.03289074 1.0000000
## QSeq10-QSeq3     1.224906e-04 -0.03259411 0.03283910 1.0000000
## QSeq100-QSeq3    1.392986e-04 -0.03257731 0.03285590 1.0000000
## QSeq100-QSeq10   1.680797e-05 -0.03269980 0.03273341 1.0000000

summary(aov(permanova.model10CVLevels.env2$value~permanova.model10CVLevels.env2$Level*permanova.model10CVLevels.env2$variable))

##                                                                               Df
## permanova.model10CVLevels.env2$Level                                           1
## permanova.model10CVLevels.env2$variable                                        6
## permanova.model10CVLevels.env2$Level:permanova.model10CVLevels.env2$variable   6
## Residuals                                                                    336
##                                                                              Sum Sq
## permanova.model10CVLevels.env2$Level                                         0.0917
## permanova.model10CVLevels.env2$variable                                      1.7809
## permanova.model10CVLevels.env2$Level:permanova.model10CVLevels.env2$variable 0.2365
## Residuals                                                                    1.5862
##                                                                              Mean Sq
## permanova.model10CVLevels.env2$Level                                         0.09171
## permanova.model10CVLevels.env2$variable                                      0.29682
## permanova.model10CVLevels.env2$Level:permanova.model10CVLevels.env2$variable 0.03941
## Residuals                                                                    0.00472
##                                                                              F value
## permanova.model10CVLevels.env2$Level                                          19.427
## permanova.model10CVLevels.env2$variable                                       62.873
## permanova.model10CVLevels.env2$Level:permanova.model10CVLevels.env2$variable   8.348
## Residuals                                                                           
##                                                                                Pr(>F)
## permanova.model10CVLevels.env2$Level                                         1.41e-05
## permanova.model10CVLevels.env2$variable                                       < 2e-16
## permanova.model10CVLevels.env2$Level:permanova.model10CVLevels.env2$variable 1.90e-08
## Residuals                                                                            
##                                                                                 
## permanova.model10CVLevels.env2$Level                                         ***
## permanova.model10CVLevels.env2$variable                                      ***
## permanova.model10CVLevels.env2$Level:permanova.model10CVLevels.env2$variable ***
## Residuals                                                                       
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

TukeyHSD(aov(permanova.model10CVLevels.env2$value~permanova.model10CVLevels.env2$Level*permanova.model10CVLevels.env2$variable))

## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## permanova.model10CVLevels.env2$Level

## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## permanova.model10CVLevels.env2$Level, permanova.model10CVLevels.env2$variable

## Warning in TukeyHSD.aov(aov(permanova.model10CVLevels.env2$value ~
## permanova.model10CVLevels.env2$Level * : 'which' specified some non-factors
## which will be dropped

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = permanova.model10CVLevels.env2$value ~ permanova.model10CVLevels.env2$Level * permanova.model10CVLevels.env2$variable)
## 
## $`permanova.model10CVLevels.env2$variable`
##                          diff         lwr        upr     p adj
## QSeq0.5-raw      2.026056e-01  0.16184313 0.24336797 0.0000000
## QSeq1-raw        2.038560e-01  0.16309363 0.24461847 0.0000000
## QSeq2-raw        2.041906e-01  0.16342815 0.24495299 0.0000000
## QSeq3-raw        2.040283e-01  0.16326583 0.24479067 0.0000000
## QSeq10-raw       2.041921e-01  0.16342968 0.24495453 0.0000000
## QSeq100-raw      2.041991e-01  0.16343667 0.24496151 0.0000000
## QSeq1-QSeq0.5    1.250498e-03 -0.03951192 0.04201292 1.0000000
## QSeq2-QSeq0.5    1.585022e-03 -0.03917740 0.04234744 0.9999998
## QSeq3-QSeq0.5    1.422700e-03 -0.03933972 0.04218512 0.9999999
## QSeq10-QSeq0.5   1.586552e-03 -0.03917587 0.04234897 0.9999998
## QSeq100-QSeq0.5  1.593538e-03 -0.03916888 0.04235596 0.9999998
## QSeq2-QSeq1      3.345237e-04 -0.04042790 0.04109695 1.0000000
## QSeq3-QSeq1      1.722021e-04 -0.04059022 0.04093462 1.0000000
## QSeq10-QSeq1     3.360543e-04 -0.04042637 0.04109848 1.0000000
## QSeq100-QSeq1    3.430403e-04 -0.04041938 0.04110546 1.0000000
## QSeq3-QSeq2     -1.623216e-04 -0.04092474 0.04060010 1.0000000
## QSeq10-QSeq2     1.530680e-06 -0.04076089 0.04076395 1.0000000
## QSeq100-QSeq2    8.516614e-06 -0.04075391 0.04077094 1.0000000
## QSeq10-QSeq3     1.638523e-04 -0.04059857 0.04092627 1.0000000
## QSeq100-QSeq3    1.708382e-04 -0.04059158 0.04093326 1.0000000
## QSeq100-QSeq10   6.985934e-06 -0.04075544 0.04076941 1.0000000

summary(aov(permanova.model10CVLevels.env3$value~permanova.model10CVLevels.env3$Level*permanova.model10CVLevels.env3$variable))

##                                                                               Df
## permanova.model10CVLevels.env3$Level                                           1
## permanova.model10CVLevels.env3$variable                                        6
## permanova.model10CVLevels.env3$Level:permanova.model10CVLevels.env3$variable   6
## Residuals                                                                    336
##                                                                              Sum Sq
## permanova.model10CVLevels.env3$Level                                         0.2228
## permanova.model10CVLevels.env3$variable                                      1.7409
## permanova.model10CVLevels.env3$Level:permanova.model10CVLevels.env3$variable 0.4492
## Residuals                                                                    0.8949
##                                                                              Mean Sq
## permanova.model10CVLevels.env3$Level                                         0.22276
## permanova.model10CVLevels.env3$variable                                      0.29015
## permanova.model10CVLevels.env3$Level:permanova.model10CVLevels.env3$variable 0.07487
## Residuals                                                                    0.00266
##                                                                              F value
## permanova.model10CVLevels.env3$Level                                           83.63
## permanova.model10CVLevels.env3$variable                                       108.93
## permanova.model10CVLevels.env3$Level:permanova.model10CVLevels.env3$variable   28.11
## Residuals                                                                           
##                                                                              Pr(>F)
## permanova.model10CVLevels.env3$Level                                         <2e-16
## permanova.model10CVLevels.env3$variable                                      <2e-16
## permanova.model10CVLevels.env3$Level:permanova.model10CVLevels.env3$variable <2e-16
## Residuals                                                                          
##                                                                                 
## permanova.model10CVLevels.env3$Level                                         ***
## permanova.model10CVLevels.env3$variable                                      ***
## permanova.model10CVLevels.env3$Level:permanova.model10CVLevels.env3$variable ***
## Residuals                                                                       
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

TukeyHSD(aov(permanova.model10CVLevels.env3$value~permanova.model10CVLevels.env3$Level*permanova.model10CVLevels.env3$variable))

## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## permanova.model10CVLevels.env3$Level

## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## permanova.model10CVLevels.env3$Level, permanova.model10CVLevels.env3$variable

## Warning in TukeyHSD.aov(aov(permanova.model10CVLevels.env3$value ~
## permanova.model10CVLevels.env3$Level * : 'which' specified some non-factors
## which will be dropped

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = permanova.model10CVLevels.env3$value ~ permanova.model10CVLevels.env3$Level * permanova.model10CVLevels.env3$variable)
## 
## $`permanova.model10CVLevels.env3$variable`
##                          diff         lwr        upr     p adj
## QSeq0.5-raw      2.007164e-01  0.17009861 0.23133426 0.0000000
## QSeq1-raw        2.015977e-01  0.17097990 0.23221554 0.0000000
## QSeq2-raw        2.019095e-01  0.17129167 0.23252732 0.0000000
## QSeq3-raw        2.016198e-01  0.17100197 0.23223762 0.0000000
## QSeq10-raw       2.017276e-01  0.17110981 0.23234545 0.0000000
## QSeq100-raw      2.016901e-01  0.17107231 0.23230795 0.0000000
## QSeq1-QSeq0.5    8.812880e-04 -0.02973654 0.03149911 1.0000000
## QSeq2-QSeq0.5    1.193061e-03 -0.02942476 0.03181088 0.9999998
## QSeq3-QSeq0.5    9.033652e-04 -0.02971446 0.03152119 1.0000000
## QSeq10-QSeq0.5   1.011197e-03 -0.02960663 0.03162902 0.9999999
## QSeq100-QSeq0.5  9.736974e-04 -0.02964413 0.03159152 0.9999999
## QSeq2-QSeq1      3.117726e-04 -0.03030605 0.03092960 1.0000000
## QSeq3-QSeq1      2.207723e-05 -0.03059575 0.03063990 1.0000000
## QSeq10-QSeq1     1.299086e-04 -0.03048791 0.03074773 1.0000000
## QSeq100-QSeq1    9.240946e-05 -0.03052541 0.03071023 1.0000000
## QSeq3-QSeq2     -2.896954e-04 -0.03090752 0.03032813 1.0000000
## QSeq10-QSeq2    -1.818641e-04 -0.03079969 0.03043596 1.0000000
## QSeq100-QSeq2   -2.193632e-04 -0.03083719 0.03039846 1.0000000
## QSeq10-QSeq3     1.078313e-04 -0.03050999 0.03072565 1.0000000
## QSeq100-QSeq3    7.033223e-05 -0.03054749 0.03068816 1.0000000
## QSeq100-QSeq10  -3.749910e-05 -0.03065532 0.03058032 1.0000000

summary(aov(permanova.model10CVLevels.env4$value~permanova.model10CVLevels.env4$Level*permanova.model10CVLevels.env4$variable))

##                                                                               Df
## permanova.model10CVLevels.env4$Level                                           1
## permanova.model10CVLevels.env4$variable                                        6
## permanova.model10CVLevels.env4$Level:permanova.model10CVLevels.env4$variable   6
## Residuals                                                                    336
##                                                                              Sum Sq
## permanova.model10CVLevels.env4$Level                                          0.003
## permanova.model10CVLevels.env4$variable                                       0.259
## permanova.model10CVLevels.env4$Level:permanova.model10CVLevels.env4$variable  0.006
## Residuals                                                                     4.262
##                                                                              Mean Sq
## permanova.model10CVLevels.env4$Level                                         0.00328
## permanova.model10CVLevels.env4$variable                                      0.04320
## permanova.model10CVLevels.env4$Level:permanova.model10CVLevels.env4$variable 0.00105
## Residuals                                                                    0.01268
##                                                                              F value
## permanova.model10CVLevels.env4$Level                                           0.259
## permanova.model10CVLevels.env4$variable                                        3.406
## permanova.model10CVLevels.env4$Level:permanova.model10CVLevels.env4$variable   0.083
## Residuals                                                                           
##                                                                               Pr(>F)
## permanova.model10CVLevels.env4$Level                                         0.61146
## permanova.model10CVLevels.env4$variable                                      0.00282
## permanova.model10CVLevels.env4$Level:permanova.model10CVLevels.env4$variable 0.99785
## Residuals                                                                           
##                                                                                
## permanova.model10CVLevels.env4$Level                                           
## permanova.model10CVLevels.env4$variable                                      **
## permanova.model10CVLevels.env4$Level:permanova.model10CVLevels.env4$variable   
## Residuals                                                                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

TukeyHSD(aov(permanova.model10CVLevels.env4$value~permanova.model10CVLevels.env4$Level*permanova.model10CVLevels.env4$variable))

## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## permanova.model10CVLevels.env4$Level

## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## permanova.model10CVLevels.env4$Level, permanova.model10CVLevels.env4$variable

## Warning in TukeyHSD.aov(aov(permanova.model10CVLevels.env4$value ~
## permanova.model10CVLevels.env4$Level * : 'which' specified some non-factors
## which will be dropped

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = permanova.model10CVLevels.env4$value ~ permanova.model10CVLevels.env4$Level * permanova.model10CVLevels.env4$variable)
## 
## $`permanova.model10CVLevels.env4$variable`
##                          diff         lwr        upr     p adj
## QSeq0.5-raw      7.992923e-02  0.01311574 0.14674273 0.0079832
## QSeq1-raw        7.737040e-02  0.01055690 0.14418389 0.0117590
## QSeq2-raw        7.681439e-02  0.01000089 0.14362788 0.0127681
## QSeq3-raw        7.735739e-02  0.01054390 0.14417089 0.0117817
## QSeq10-raw       7.742544e-02  0.01061195 0.14423894 0.0116631
## QSeq100-raw      7.743403e-02  0.01062054 0.14424753 0.0116482
## QSeq1-QSeq0.5   -2.558835e-03 -0.06937233 0.06425466 0.9999998
## QSeq2-QSeq0.5   -3.114845e-03 -0.06992834 0.06369865 0.9999994
## QSeq3-QSeq0.5   -2.571840e-03 -0.06938533 0.06424166 0.9999998
## QSeq10-QSeq0.5  -2.503787e-03 -0.06931728 0.06430971 0.9999998
## QSeq100-QSeq0.5 -2.495198e-03 -0.06930869 0.06431830 0.9999998
## QSeq2-QSeq1     -5.560095e-04 -0.06736950 0.06625749 1.0000000
## QSeq3-QSeq1     -1.300446e-05 -0.06682650 0.06680049 1.0000000
## QSeq10-QSeq1     5.504873e-05 -0.06675845 0.06686854 1.0000000
## QSeq100-QSeq1    6.363769e-05 -0.06674986 0.06687713 1.0000000
## QSeq3-QSeq2      5.430050e-04 -0.06627049 0.06735650 1.0000000
## QSeq10-QSeq2     6.110582e-04 -0.06620244 0.06742455 1.0000000
## QSeq100-QSeq2    6.196471e-04 -0.06619385 0.06743314 1.0000000
## QSeq10-QSeq3     6.805319e-05 -0.06674544 0.06688155 1.0000000
## QSeq100-QSeq3    7.664215e-05 -0.06673685 0.06689014 1.0000000
## QSeq100-QSeq10   8.588960e-06 -0.06680491 0.06682208 1.0000000

summary(aov(permanova.model10CVLevels.env5$value~permanova.model10CVLevels.env5$Level*permanova.model10CVLevels.env5$variable))

##                                                                               Df
## permanova.model10CVLevels.env5$Level                                           1
## permanova.model10CVLevels.env5$variable                                        6
## permanova.model10CVLevels.env5$Level:permanova.model10CVLevels.env5$variable   6
## Residuals                                                                    336
##                                                                              Sum Sq
## permanova.model10CVLevels.env5$Level                                          0.211
## permanova.model10CVLevels.env5$variable                                       0.781
## permanova.model10CVLevels.env5$Level:permanova.model10CVLevels.env5$variable  0.544
## Residuals                                                                     7.748
##                                                                              Mean Sq
## permanova.model10CVLevels.env5$Level                                         0.21103
## permanova.model10CVLevels.env5$variable                                      0.13009
## permanova.model10CVLevels.env5$Level:permanova.model10CVLevels.env5$variable 0.09065
## Residuals                                                                    0.02306
##                                                                              F value
## permanova.model10CVLevels.env5$Level                                           9.152
## permanova.model10CVLevels.env5$variable                                        5.642
## permanova.model10CVLevels.env5$Level:permanova.model10CVLevels.env5$variable   3.931
## Residuals                                                                           
##                                                                                Pr(>F)
## permanova.model10CVLevels.env5$Level                                          0.00268
## permanova.model10CVLevels.env5$variable                                      1.34e-05
## permanova.model10CVLevels.env5$Level:permanova.model10CVLevels.env5$variable  0.00082
## Residuals                                                                            
##                                                                                 
## permanova.model10CVLevels.env5$Level                                         ** 
## permanova.model10CVLevels.env5$variable                                      ***
## permanova.model10CVLevels.env5$Level:permanova.model10CVLevels.env5$variable ***
## Residuals                                                                       
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

TukeyHSD(aov(permanova.model10CVLevels.env5$value~permanova.model10CVLevels.env5$Level*permanova.model10CVLevels.env5$variable))

## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## permanova.model10CVLevels.env5$Level

## Warning in replications(paste("~", xx), data = mf): non-factors ignored:
## permanova.model10CVLevels.env5$Level, permanova.model10CVLevels.env5$variable

## Warning in TukeyHSD.aov(aov(permanova.model10CVLevels.env5$value ~
## permanova.model10CVLevels.env5$Level * : 'which' specified some non-factors
## which will be dropped

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = permanova.model10CVLevels.env5$value ~ permanova.model10CVLevels.env5$Level * permanova.model10CVLevels.env5$variable)
## 
## $`permanova.model10CVLevels.env5$variable`
##                          diff         lwr        upr     p adj
## QSeq0.5-raw      1.349313e-01  0.04484332 0.22501925 0.0002421
## QSeq1-raw        1.352374e-01  0.04514948 0.22532541 0.0002317
## QSeq2-raw        1.343638e-01  0.04427584 0.22445178 0.0002624
## QSeq3-raw        1.353955e-01  0.04530749 0.22548342 0.0002266
## QSeq10-raw       1.349400e-01  0.04485204 0.22502797 0.0002418
## QSeq100-raw      1.348424e-01  0.04475439 0.22493032 0.0002452
## QSeq1-QSeq0.5    3.061568e-04 -0.08978181 0.09039412 1.0000000
## QSeq2-QSeq0.5   -5.674746e-04 -0.09065544 0.08952049 1.0000000
## QSeq3-QSeq0.5    4.641732e-04 -0.08962379 0.09055214 1.0000000
## QSeq10-QSeq0.5   8.719429e-06 -0.09007925 0.09009669 1.0000000
## QSeq100-QSeq0.5 -8.893162e-05 -0.09017690 0.08999903 1.0000000
## QSeq2-QSeq1     -8.736314e-04 -0.09096160 0.08921433 1.0000000
## QSeq3-QSeq1      1.580164e-04 -0.08992995 0.09024598 1.0000000
## QSeq10-QSeq1    -2.974374e-04 -0.09038540 0.08979053 1.0000000
## QSeq100-QSeq1   -3.950884e-04 -0.09048305 0.08969288 1.0000000
## QSeq3-QSeq2      1.031648e-03 -0.08905632 0.09111961 1.0000000
## QSeq10-QSeq2     5.761940e-04 -0.08951177 0.09066416 1.0000000
## QSeq100-QSeq2    4.785430e-04 -0.08960942 0.09056651 1.0000000
## QSeq10-QSeq3    -4.554538e-04 -0.09054342 0.08963251 1.0000000
## QSeq100-QSeq3   -5.531048e-04 -0.09064107 0.08953486 1.0000000
## QSeq100-QSeq10  -9.765105e-05 -0.09018562 0.08999032 1.0000000

leveneTest(permanova.model10CVLevels.model$value~permanova.model10CVLevels.model$variable)

## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value Pr(>F)
## group   6  0.0147      1
##       343

leveneTest(permanova.model10CVLevels.env1$value~permanova.model10CVLevels.env1$variable)

## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value    Pr(>F)    
## group   6  41.537 < 2.2e-16 ***
##       343                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

leveneTest(permanova.model10CVLevels.env2$value~permanova.model10CVLevels.env2$variable)

## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value    Pr(>F)    
## group   6  56.935 < 2.2e-16 ***
##       343                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

leveneTest(permanova.model10CVLevels.env3$value~permanova.model10CVLevels.env3$variable)

## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value    Pr(>F)    
## group   6  95.357 < 2.2e-16 ***
##       343                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

leveneTest(permanova.model10CVLevels.env4$value~permanova.model10CVLevels.env4$variable)

## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value    Pr(>F)    
## group   6  32.326 < 2.2e-16 ***
##       343                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

leveneTest(permanova.model10CVLevels.env5$value~permanova.model10CVLevels.env5$variable)

## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value    Pr(>F)    
## group   6  18.764 < 2.2e-16 ***
##       343                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Conclusions:

1. Performance of all methods is highest at low sparcity, high sampling depth, and low sampling variance.

2. Model.Microbiome provides an empirical framework for optimizing sequence count normalization methods prior to making ecological inferences; in our example the parameters for QSeq0.5 resulted in a consistent underperformance compared to other parameters.

Network Analysis

Model.Microbiome constructs networks and network plots using two heuristics for creating the network thresholds. It also includes some functions to simplify accessing the network statistics that have been calculated, and plots that are generated. These are illustrated in the example below. These networks are built using two alternative approaches. Whenever we build a network, we need to establish a threshold to determine what relationships we consider significant to include. Our two methods include one that is a static threshold value, set at a correlation coefficient of 0.8; the other is a dynamic threshold heuristic that identifies the maximum threshold value that results in a network with 250 edges. The reason we include the secon method is because the network statistics for two graphs with different number of edges are in principle not comparable. However, we have found that in ecological settings that while the metrics we use might change, the overall interpretation of each plot does not. We also find that similar to other measures of beta diversity (here interpreted as changing species associations across sites), that statistics derived from the network are sensitive to network construction method, but are robust to normalization methods of the community. Let’s take a look an an example using the community structure example from earlier in the tutorial:

method3<-c("model", "raw", "QSeq0.5", "QSeq10")

plotstats.A<-getNetStats(model10.A, method3) # get statistics

## [1] 4
## [1] 0.410976
## [1] 0.358304
## [1] 0.3624654
## [1] 0.358304
## [1] 0.3843079
## [1] 0.3998413
## [1] 0.4045508
## [1] 0.3998413
## [1] 0.3866272
## [1] 0.4247437
## [1] 0.4294848
## [1] 0.4247437
## [1] 0.2361243
## [1] 0.2167414
## [1] 0.2167414
## [1] 0.2167414
## [1] 0.4499039
## [1] 0.4329779
## [1] 0.4579468
## [1] 0.4329779
## [1] 0.461248
## [1] 0.477312
## [1] 0.471168
## [1] 0.477312
## [1] 0.2728415
## [1] 0.1432485
## [1] 0.1702268
## [1] 0.1407465
## [1] 0.248736
## [1] 0.2950365
## [1] 0.289536
## [1] 0.2950365
## [1] 0.2729277
## [1] 0.243103
## [1] 0.245344
## [1] 0.243103
## [1] 0.5104065
## [1] 0.5656
## [1] 0.5603943
## [1] 0.5656

plotstats.A$D.module.table # modularity value table for dynamic threshold

##            model       raw   QSeq0.5    QSeq10
## rep 1  0.4109760 0.3583040 0.3624654 0.3583040
## rep 2  0.3843079 0.3998413 0.4045508 0.3998413
## rep 3  0.3866272 0.4247437 0.4294848 0.4247437
## rep 4  0.2361243 0.2167414 0.2167414 0.2167414
## rep 5  0.4499039 0.4329779 0.4579468 0.4329779
## rep 6  0.4612480 0.4773120 0.4711680 0.4773120
## rep 7  0.2728415 0.1432485 0.1702268 0.1407465
## rep 8  0.2487360 0.2950365 0.2895360 0.2950365
## rep 9  0.2729277 0.2431030 0.2453440 0.2431030
## rep 10 0.5104065 0.5656000 0.5603943 0.5656000

plotstats.A$S.module.table # modularity value table for static threshold

##             model        raw    QSeq0.5     QSeq10
## rep 1  0.09944751 0.10169492 0.10000000 0.10169492
## rep 2  0.04097614 0.03657802 0.03512783 0.03657802
## rep 3  0.09493751 0.10342449 0.10342449 0.10342449
## rep 4  0.02987515 0.03089773 0.02550441 0.03089773
## rep 5  0.13171200 0.13817258 0.13714286 0.13817258
## rep 6  0.26509864 0.27045830 0.27191176 0.27045830
## rep 7  0.00000000 0.00000000 0.00000000 0.00000000
## rep 8  0.32680079 0.35605760 0.35605760 0.35605760
## rep 9  0.10811033 0.10957908 0.11389167 0.10957908
## rep 10 0.06818182 0.07692308 0.07692308 0.07692308

A close look at the module table suggests that the characteristics of the un-noralized dataset are driving the network statistics of the normalized set. For example, if we look at rep1, the values for QSeq0.5 and QSeq10 are both close or identical to the values for the raw dataset. This means that this normalization technique is not necessarily improving the accuracy of the network statistics. We can see this pattern does not depend on whether the network is constructed using a dynamic or static threshold. We can look at the threshold cutoff for the dynamic network construction to see if there are any patterns:

plotstats.A$D.Threshold.table # table of threshold values for dynamic threshold

##        model   raw QSeq0.5 QSeq10
## rep 1  0.955 0.944   0.943  0.944
## rep 2  0.982 0.980   0.980  0.980
## rep 3  0.978 0.975   0.975  0.975
## rep 4  0.988 0.987   0.987  0.987
## rep 5  0.970 0.962   0.962  0.962
## rep 6  0.932 0.929   0.929  0.929
## rep 7  0.998 0.997   0.997  0.997
## rep 8  0.731 0.712   0.714  0.712
## rep 9  0.972 0.966   0.966  0.966
## rep 10 0.982 0.977   0.976  0.977

As before the QSeq methods do not provide an improvement over the raw dataset. We can use this method to look at differences in internal structure. The pattern is the same:

plotstats.B<-getNetStats(model10.B, method3) # get statistics

## [1] 4
## [1] 0.4771983
## [1] 0.437088
## [1] 0.4297682
## [1] 0.437088
## [1] 0.643872
## [1] 0.643872
## [1] 0.643872
## [1] 0.643872
## [1] 0.353504
## [1] 0.324192
## [1] 0.324192
## [1] 0.324192
## [1] 0.260736
## [1] 0.2855883
## [1] 0.2917726
## [1] 0.2855883
## [1] 0.268128
## [1] 0.293312
## [1] 0.293312
## [1] 0.293312
## [1] 0.3045163
## [1] 0.300704
## [1] 0.300704
## [1] 0.300704
## [1] 0.311319
## [1] 0.354592
## [1] 0.3487969
## [1] 0.354592
## [1] 0.333184
## [1] 0.349888
## [1] 0.349888
## [1] 0.349888
## [1] 0.317536
## [1] 0.280896
## [1] 0.280896
## [1] 0.280896
## [1] 0.488352
## [1] 0.497184
## [1] 0.497184
## [1] 0.497184

plotstats.B$D.module.table # modularity value table for dynamic threshold

##            model       raw   QSeq0.5    QSeq10
## rep 1  0.4771983 0.4370880 0.4297682 0.4370880
## rep 2  0.6438720 0.6438720 0.6438720 0.6438720
## rep 3  0.3535040 0.3241920 0.3241920 0.3241920
## rep 4  0.2607360 0.2855883 0.2917726 0.2855883
## rep 5  0.2681280 0.2933120 0.2933120 0.2933120
## rep 6  0.3045163 0.3007040 0.3007040 0.3007040
## rep 7  0.3113190 0.3545920 0.3487969 0.3545920
## rep 8  0.3331840 0.3498880 0.3498880 0.3498880
## rep 9  0.3175360 0.2808960 0.2808960 0.2808960
## rep 10 0.4883520 0.4971840 0.4971840 0.4971840

plotstats.B$D.Threshold.table # table of threshold values for dynamic threshold

##        model   raw QSeq0.5 QSeq10
## rep 1  0.953 0.949   0.949  0.949
## rep 2  0.414 0.392   0.382  0.392
## rep 3  0.893 0.892   0.892  0.892
## rep 4  0.977 0.967   0.967  0.967
## rep 5  0.802 0.799   0.800  0.799
## rep 6  0.924 0.921   0.921  0.920
## rep 7  0.963 0.962   0.961  0.962
## rep 8  0.894 0.897   0.892  0.897
## rep 9  0.929 0.941   0.937  0.941
## rep 10 0.081 0.083   0.084  0.084

plotstats.B$S.module.table # modularity value table for static threshold

##             model        raw    QSeq0.5     QSeq10
## rep 1  0.11114921 0.12333215 0.12505602 0.12333215
## rep 2  0.74710648 0.74133333 0.73440000 0.74133333
## rep 3  0.12431002 0.14444288 0.14296729 0.14444288
## rep 4  0.04015084 0.05331283 0.05331283 0.05331283
## rep 5  0.26812800 0.29331200 0.29331200 0.29331200
## rep 6  0.17940219 0.17437673 0.17376731 0.17437673
## rep 7  0.24861363 0.24861363 0.24861363 0.24861363
## rep 8  0.32632674 0.32453978 0.32632674 0.32453978
## rep 9  0.30511937 0.31266437 0.31266437 0.30887663
## rep 10 0.78710744 0.78826531 0.79316713 0.78826531

plotstats.B$S.Threshold.table # table of threshold values for static threshold (0.8)

##        model raw QSeq0.5 QSeq10
## rep 1    0.8 0.8     0.8    0.8
## rep 2    0.8 0.8     0.8    0.8
## rep 3    0.8 0.8     0.8    0.8
## rep 4    0.8 0.8     0.8    0.8
## rep 5    0.8 0.8     0.8    0.8
## rep 6    0.8 0.8     0.8    0.8
## rep 7    0.8 0.8     0.8    0.8
## rep 8    0.8 0.8     0.8    0.8
## rep 9    0.8 0.8     0.8    0.8
## rep 10   0.8 0.8     0.8    0.8

plotstats.C<-getNetStats(model10.C, method3) # get statistics

## [1] 4
## [1] 0.439264
## [1] 0.439264
## [1] 0.439264
## [1] 0.433327
## [1] 0.369088
## [1] 0.39248
## [1] 0.39248
## [1] 0.39248
## [1] 0.531808
## [1] 0.529248
## [1] 0.533152
## [1] 0.529248
## [1] 0.5050391
## [1] 0.4929453
## [1] 0.486236
## [1] 0.4929453
## [1] 0.422784
## [1] 0.42864
## [1] 0.4032
## [1] 0.42864
## [1] 0.393487
## [1] 0.3870622
## [1] 0.3870622
## [1] 0.3870622
## [1] 0.492
## [1] 0.4745528
## [1] 0.475776
## [1] 0.481184
## [1] 0.4798279
## [1] 0.4735569
## [1] 0.46755
## [1] 0.4735569
## [1] 0.467456
## [1] 0.43392
## [1] 0.43392
## [1] 0.43392
## [1] 0.392256
## [1] 0.3770156
## [1] 0.381012
## [1] 0.3770156

plotstats.C$D.module.table # modularity value table for dynamic threshold

##            model       raw   QSeq0.5    QSeq10
## rep 1  0.4392640 0.4392640 0.4392640 0.4333270
## rep 2  0.3690880 0.3924800 0.3924800 0.3924800
## rep 3  0.5318080 0.5292480 0.5331520 0.5292480
## rep 4  0.5050391 0.4929453 0.4862360 0.4929453
## rep 5  0.4227840 0.4286400 0.4032000 0.4286400
## rep 6  0.3934870 0.3870622 0.3870622 0.3870622
## rep 7  0.4920000 0.4745528 0.4757760 0.4811840
## rep 8  0.4798279 0.4735569 0.4675500 0.4735569
## rep 9  0.4674560 0.4339200 0.4339200 0.4339200
## rep 10 0.3922560 0.3770156 0.3810120 0.3770156

plotstats.C$D.Threshold.table # table of threshold values for dynamic threshold

##        model   raw       QSeq0.5 QSeq10
## rep 1  0.160 0.160  1.570000e-01  0.159
## rep 2  0.730 0.717  7.170000e-01  0.717
## rep 3  0.074 0.078  8.300000e-02  0.078
## rep 4  0.039 0.039  3.800000e-02  0.039
## rep 5  0.607 0.651  6.440000e-01  0.651
## rep 6  0.142 0.151  1.510000e-01  0.151
## rep 7  0.066 0.082  8.200000e-02  0.083
## rep 8  0.001 0.004  3.000000e-03  0.004
## rep 9  0.809 0.801  8.000000e-01  0.801
## rep 10 0.001 0.001 -8.812395e-16  0.001

plotstats.C$S.module.table # modularity value table for static threshold

##            model       raw   QSeq0.5    QSeq10
## rep 1  0.7957064 0.8040816 0.8040816 0.8040816
## rep 2  0.4786784 0.4952257 0.4952257 0.4952257
## rep 3  0.8510742 0.8616667 0.8616667 0.8616667
## rep 4  0.7958478 0.7865014 0.7865014 0.7865014
## rep 5  0.6811435 0.6722044 0.6765062 0.6722044
## rep 6  0.8126722 0.8028571 0.8028571 0.8028571
## rep 7  0.8144290 0.8144290 0.8144290 0.8144290
## rep 8  0.7566163 0.7474074 0.7474074 0.7474074
## rep 9  0.4533535 0.4322339 0.4391534 0.4322339
## rep 10 0.9149660 0.9152893 0.9251701 0.9152893

plotstats.C$S.Threshold.table # table of threshold values for static threshold (0.8)

##        model raw QSeq0.5 QSeq10
## rep 1    0.8 0.8     0.8    0.8
## rep 2    0.8 0.8     0.8    0.8
## rep 3    0.8 0.8     0.8    0.8
## rep 4    0.8 0.8     0.8    0.8
## rep 5    0.8 0.8     0.8    0.8
## rep 6    0.8 0.8     0.8    0.8
## rep 7    0.8 0.8     0.8    0.8
## rep 8    0.8 0.8     0.8    0.8
## rep 9    0.8 0.8     0.8    0.8
## rep 10   0.8 0.8     0.8    0.8

plotstats.D<-getNetStats(model10.D, method3) # get statistics

## [1] 4
## [1] 0.340544
## [1] 0.343392
## [1] 0.343392
## [1] 0.343392
## [1] 0.5121567
## [1] 0.519968
## [1] 0.524224
## [1] 0.519968
## [1] 0.441568
## [1] 0.449408
## [1] 0.448224
## [1] 0.449408
## [1] 0
## [1] 0
## [1] 0
## [1] 0
## [1] 0.324288
## [1] 0.344608
## [1] 0.349792
## [1] 0.344608
## [1] 0
## [1] 0
## [1] 0
## [1] 0
## [1] 0.490848
## [1] 0.475386
## [1] 0.467104
## [1] 0.475386
## [1] 0.321568
## [1] 0.304128
## [1] 0.304128
## [1] 0.304128
## [1] 0.486912
## [1] 0.490784
## [1] 0.490784
## [1] 0.490784
## [1] 0
## [1] 0
## [1] 0
## [1] 0

plotstats.D$D.module.table # modularity value table for dynamic threshold

##            model      raw  QSeq0.5   QSeq10
## rep 1  0.3405440 0.343392 0.343392 0.343392
## rep 2  0.5121567 0.519968 0.524224 0.519968
## rep 3  0.4415680 0.449408 0.448224 0.449408
## rep 4  0.0000000 0.000000 0.000000 0.000000
## rep 5  0.3242880 0.344608 0.349792 0.344608
## rep 6  0.0000000 0.000000 0.000000 0.000000
## rep 7  0.4908480 0.475386 0.467104 0.475386
## rep 8  0.3215680 0.304128 0.304128 0.304128
## rep 9  0.4869120 0.490784 0.490784 0.490784
## rep 10 0.0000000 0.000000 0.000000 0.000000

plotstats.D$D.Threshold.table # table of threshold values for dynamic threshold

##         model    raw QSeq0.5 QSeq10
## rep 1   0.681  0.680   0.681  0.680
## rep 2   0.125  0.108   0.121  0.109
## rep 3   0.089  0.092   0.090  0.092
## rep 4  -0.001 -0.001  -0.001 -0.001
## rep 5   0.675  0.657   0.656  0.657
## rep 6  -0.001 -0.001  -0.001 -0.001
## rep 7   0.004  0.004   0.007  0.004
## rep 8   0.687  0.670   0.671  0.670
## rep 9   0.622  0.614   0.614  0.614
## rep 10 -0.001 -0.001  -0.001 -0.001

plotstats.D$S.module.table # modularity value table for static threshold

##            model       raw   QSeq0.5    QSeq10
## rep 1  0.4815760 0.4912190 0.4838156 0.4912190
## rep 2  0.5682973 0.5682973 0.5682973 0.5682973
## rep 3  0.8097826 0.8097826 0.8034568 0.8097826
## rep 4  0.7992304 0.7903646 0.7903646 0.7903646
## rep 5  0.6353308 0.6320232 0.6358643 0.6320232
## rep 6  0.7210884 0.7210884 0.7210884 0.7210884
## rep 7  0.8008163 0.7919550 0.7919550 0.7919550
## rep 8  0.5468444 0.5562307 0.5682404 0.5562307
## rep 9  0.6132653 0.6253061 0.6253061 0.6253061
## rep 10 0.7761341 0.7761341 0.7761341 0.7761341

plotstats.D$S.Threshold.table # table of threshold values for static threshold (0.8)

##        model raw QSeq0.5 QSeq10
## rep 1    0.8 0.8     0.8    0.8
## rep 2    0.8 0.8     0.8    0.8
## rep 3    0.8 0.8     0.8    0.8
## rep 4    0.8 0.8     0.8    0.8
## rep 5    0.8 0.8     0.8    0.8
## rep 6    0.8 0.8     0.8    0.8
## rep 7    0.8 0.8     0.8    0.8
## rep 8    0.8 0.8     0.8    0.8
## rep 9    0.8 0.8     0.8    0.8
## rep 10   0.8 0.8     0.8    0.8

What this tells us is that this normalization technique does not have a large influence on the overall modularity statistic for the network; it does not improve our ability to identify clusters of associating or dissociating taxa. These metrics may still be useful in the case that methods are identified that do significantly improve the accuracy of replicating the network structure from before sampling; or in identifying cases where a normalization technique significantly decreases the accuracy of replicating the network structure from before sampling.

We can also visualize the plots:

getNetPlot(model10.A[1],method3)

Some figures from the data for the paper:

Figure 4

In each experiment, LII

ggplot(model10Levels.summary1[model10Levels.summary1$variable == "raw"|
                                model10Levels.summary1$variable == "QSeq0.5"|
                                model10Levels.summary1$variable == "QSeq2"|
                                model10Levels.summary1$variable == "QSeq100",], aes(x=Level, y=value, group = variable, color=variable, size=1))+
  geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.2, position=position_dodge(.3), size=1) +
  #scale_colour_viridis_d(direction=-1)+
  scale_colour_grey()+
  geom_line(position=position_dodge(.3), size=1, aes(linetype=variable))+
  geom_point(position=position_dodge(.3), size=1)+
  xlab("Degree of Structure")+
  ylab("LII Value (Mean +/- standard dev)")+
  theme_classic()

#model10.SeqLevels.summary2
ggplot(model10.SeqLevels.summary[model10.SeqLevels.summary$variable == "raw"|model10.SeqLevels.summary$variable == "QSeq0.5"|model10.SeqLevels.summary$variable == "QSeq2"|model10.SeqLevels.summary$variable == "QSeq100",], aes(x=Level, y=value, group = variable, color=variable, size=1))+
  geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=100, position=position_dodge(70), size=1) +
  #scale_colour_viridis_d(direction=-1)+
  scale_colour_grey()+
  geom_line(position=position_dodge(70), size=1, aes(linetype=variable))+
  geom_point(position=position_dodge(70), size=1)+
  xlab("Sampling Depth")+
  ylab("LII Value (Mean +/- standard dev)")+
  theme_classic()

ggplot(model10.SeqVarLevels.summary[model10.SeqVarLevels.summary$variable == "raw"|
                                       model10.SeqVarLevels.summary$variable == "QSeq0.5"|
                                       model10.SeqVarLevels.summary$variable == "QSeq2"|
                                       model10.SeqVarLevels.summary$variable == "QSeq100",], aes(x=Level, y=value, group = variable, color=variable, size=1))+
  geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.08), size=1) +
  #scale_colour_viridis_d(direction=-1)+
  scale_colour_grey()+
  geom_line(position=position_dodge(.08), size=1, aes(linetype=variable))+
  geom_point(position=position_dodge(.08), size=1)+
  xlab("Relative Variance (variance / mean)")+
  ylab("LII Value (Mean +/- standard dev)")+
  theme_classic()

# Figure 3: rank abundance curve

par(mfrow=c(2,2))
barplot(sort(taxa_sums(model10.A$rep1$model$comm)/1000000, TRUE), 
    las = 2, main ="Rank Abundance Lowest Sparcity", ylab="Million Counts")
barplot(sort(taxa_sums(model10.B$rep1$model$comm)/1000000, TRUE), 
    las = 2, main ="Rank Abundance Low Sparcity", ylab="Million Counts")
barplot(sort(taxa_sums(model10.C$rep1$model$comm)/1000000, TRUE), 
    las = 2, main ="Rank Abundance  High Sparcity", ylab="Million Counts")
barplot(sort(taxa_sums(model10.D$rep1$model$comm)/1000000, TRUE), 
    las = 2, main ="Rank Abundance Highest Sparcity", ylab="Million Counts")

# figure 5

#permanova.model10CVLevels.modelP
ggplot(permanova.model10CVLevels.modelP[permanova.model10CVLevels.modelP$variable=="raw" |
                                        permanova.model10CVLevels.modelP$variable=="QSeq0.5" |
                                        permanova.model10CVLevels.modelP$variable=="QSeq2" |
                                        permanova.model10CVLevels.modelP$variable=="QSeq100",], aes(x=Level, y=value, group = variable, color=variable, size=1))+
  geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.08), size=1) +
  #scale_colour_viridis_d(direction=-1)+
  scale_colour_grey()+
  geom_line(position=position_dodge(.08), size=1, aes(linetype=variable))+
  geom_point(position=position_dodge(.08), size=1)+
  xlab("Relative Variance (variance / mean)")+
  ylab("PERMANOVA R-Squared Value (Mean +/- standard dev)")+
  ggtitle("Experimental Model")+
  theme_classic()

#permanova.model10CVLevels.modelP
ggplot(permanova.model10CVLevels.env1P[permanova.model10CVLevels.env1P$variable=="raw" |
                                        permanova.model10CVLevels.env1P$variable=="QSeq0.5" |
                                        permanova.model10CVLevels.env1P$variable=="QSeq2" |
                                        permanova.model10CVLevels.env1P$variable=="QSeq100",], aes(x=Level, y=value, group = variable, color=variable, size=1))+
  geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.08), size=1) +
  #scale_colour_viridis_d(direction=-1)+
  scale_colour_grey()+
  geom_line(position=position_dodge(.08), size=1, aes(linetype=variable))+
  geom_point(position=position_dodge(.08), size=1)+
  xlab("Relative Variance (variance / mean)")+
  ylab("PERMANOVA R-Squared Value (Mean +/- standard dev)")+
  ggtitle("Environmental Factor 1")+
  theme_classic()

#permanova.model10CVLevels.modelP
ggplot(permanova.model10CVLevels.env2P[permanova.model10CVLevels.env2P$variable=="raw" |
                                        permanova.model10CVLevels.env2P$variable=="QSeq0.5" |
                                        permanova.model10CVLevels.env2P$variable=="QSeq2" |
                                        permanova.model10CVLevels.env2P$variable=="QSeq100",], aes(x=Level, y=value, group = variable, color=variable, size=1))+
  geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.08), size=1) +
  #scale_colour_viridis_d(direction=-1)+
  scale_colour_grey()+
  geom_line(position=position_dodge(.08), size=1, aes(linetype=variable))+
  geom_point(position=position_dodge(.08), size=1)+
  xlab("Relative Variance (variance / mean)")+
  ylab("PERMANOVA R-Squared Value (Mean +/- standard dev)")+
  ggtitle("Environmental Factor 2")+
  theme_classic()

#permanova.model10CVLevels.modelP
ggplot(permanova.model10CVLevels.env3P[permanova.model10CVLevels.env3P$variable=="raw" |
                                        permanova.model10CVLevels.env3P$variable=="QSeq0.5" |
                                        permanova.model10CVLevels.env3P$variable=="QSeq2" |
                                        permanova.model10CVLevels.env3P$variable=="QSeq100",], aes(x=Level, y=value, group = variable, color=variable, size=1))+
  geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.08), size=1) +
  #scale_colour_viridis_d(direction=-1)+
  scale_colour_grey()+
  geom_line(position=position_dodge(.08), size=1, aes(linetype=variable))+
  geom_point(position=position_dodge(.08), size=1)+
  xlab("Relative Variance (variance / mean)")+
  ylab("PERMANOVA R-Squared Value (Mean +/- standard dev)")+
  ggtitle("Environmental Factor 3")+
  theme_classic()

#permanova.model10CVLevels.modelP
ggplot(permanova.model10CVLevels.env4P[permanova.model10CVLevels.env4P$variable=="raw" |
                                        permanova.model10CVLevels.env4P$variable=="QSeq0.5" |
                                        permanova.model10CVLevels.env4P$variable=="QSeq2" |
                                        permanova.model10CVLevels.env4P$variable=="QSeq100",], aes(x=Level, y=value, group = variable, color=variable, size=1))+
  geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.08), size=1) +
  #scale_colour_viridis_d(direction=-1)+
  scale_colour_grey()+
  geom_line(position=position_dodge(.08), size=1, aes(linetype=variable))+
  geom_point(position=position_dodge(.08), size=1)+
  xlab("Relative Variance (variance / mean)")+
  ylab("PERMANOVA R-Squared Value (Mean +/- standard dev)")+
  ggtitle("Environmental Factor 4")+
  theme_classic()

#permanova.model10CVLevels.modelP
ggplot(permanova.model10CVLevels.env5P[permanova.model10CVLevels.env5P$variable=="raw" |
                                        permanova.model10CVLevels.env5P$variable=="QSeq0.5" |
                                        permanova.model10CVLevels.env5P$variable=="QSeq2" |
                                        permanova.model10CVLevels.env5P$variable=="QSeq100",], aes(x=Level, y=value, group = variable, color=variable, size=1))+
  geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.08), size=1) +
  #scale_colour_viridis_d(direction=-1)+
  scale_colour_grey()+
  geom_line(position=position_dodge(.08), size=1, aes(linetype=variable))+
  geom_point(position=position_dodge(.08), size=1)+
  xlab("Relative Variance (variance / mean)")+
  ylab("PERMANOVA R-Squared Value (Mean +/- standard dev)")+
  ggtitle("Environmental Factor 5")+
  theme_classic()

# Figure 5

#SV.lmRatio.model10CV.p
ggplot(SV.lmRatio.model10CV.p[SV.lmRatio.model10CV.p$variable=="raw" |
                                        SV.lmRatio.model10CV.p$variable=="QSeq0.5" |
                                        SV.lmRatio.model10CV.p$variable=="QSeq2" |
                                        SV.lmRatio.model10CV.p$variable=="QSeq100",], aes(x=Level, y=value, group = variable, color=variable, size=1))+
  geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.08), size=1) +
  #scale_colour_viridis_d(direction=-1)+
  scale_colour_grey()+
  geom_line(position=position_dodge(.08), size=1, aes(linetype=variable))+
  geom_point(position=position_dodge(.08), size=1)+
  xlab("Relative Sampling Variance (variance / mean)")+
  ylab("Linear Model R-Ratio Variance (Mean +/- standard dev)")+
  ggtitle("Variance of Linear Model R-Ratio")+
  theme_classic()

SV.lmRatio.model10MCV.p

#SV.lmRatio.model10MCV.p
ggplot(SV.lmRatio.model10MCV.p[SV.lmRatio.model10MCV.p$variable=="raw" |
                                        SV.lmRatio.model10MCV.p$variable=="QSeq0.5" |
                                        SV.lmRatio.model10MCV.p$variable=="QSeq2" |
                                        SV.lmRatio.model10MCV.p$variable=="QSeq100",], aes(x=Level, y=value, group = variable, color=variable, size=1))+
  geom_errorbar(aes(ymin=value-sd, ymax=value+sd), width=.1, position=position_dodge(.08), size=1) +
  #scale_colour_viridis_d(direction=-1)+
  scale_colour_grey()+
  geom_line(position=position_dodge(.08), size=1, aes(linetype=variable))+
  geom_point(position=position_dodge(.08), size=1)+
  xlab("Relative Sampling Variance (variance / mean)")+
  ylab("Linear Model R-Ratio Variance (Mean +/- standard dev)")+
  ggtitle("Variance of Linear Model R-Ratio")+
  theme_classic()

#devtools::install_github("ricardo-bion/ggradar", dependencies=TRUE)
#library(ggradar)

# table of output summary

#PERMANOVA.Model
#PERMANOVA.F1
#PERMANOVA.F2
#PERMANOVA.F3
#PERMANOVA.F4
#PERMANOVA.F5

#lmRatio.model(mean)
#lmRatio.model(var)
#lmRatio.env(mean)
#lmRatio.env(var)

#taxRatio

#LII.R
#LII

#getRadar<-function(x, method){
#  Summarize.LII(x, method)
#  
#}
#Summarize.LII(model10.A, method2)
##Summarize.PERMANOVA.Rratio(model10.A, method2, "CategoryRratio")
#Summarize.PERMANOVA.Rratio(model10.A, method2, "F1Rratio")
#Summarize.PERMANOVA.Rratio(model10.A, method2, "F2Rratio")
#Summarize.PERMANOVA.Rratio(model10.A, method2, "F3Rratio")
#Summarize.PERMANOVA.Rratio(model10.A, method2, "F4Rratio")
#Summarize.PERMANOVA.Rratio(model10.A, method2, "F5Rratio")

#Summarize.lmRatiotabModel.Median(model10.A, method2)
#Summarize.lmRatiotabModel.Var(model10.A, method2)
#Summarize.lmRatiotab.Median(model10.A, method2)
#Summarize.lmRatiotab.Var(model10.A, method2)

#getTaxCor.Tab(model10.A, method2)

#Summarize.LII(model10.A, method2)

#dtest<-rbind(as.data.frame(Summarize.PERMANOVA.Rratio(model10.A, method2, "CategoryRratio")), as.data.frame(Summarize.PERMANOVA.Rratio(model10.A, method2, "F1Rratio")), as.data.frame(Summarize.PERMANOVA.Rratio(model10.A, method2, "F2Rratio")), as.data.frame(Summarize.PERMANOVA.Rratio(model10.A, method2, "F3Rratio")), as.data.frame(Summarize.PERMANOVA.Rratio(model10.A, method2, "F4Rratio")), as.data.frame(Summarize.PERMANOVA.Rratio(model10.A, method2, "F5Rratio")), as.data.frame(Summarize.lmRatiotabModel.Median(model10.A, method2)), as.data.frame(Summarize.lmRatiotabModel.Var(model10.A, method2)), as.data.frame(Summarize.lmRatiotab.Median(model10.A, method2)), as.data.frame(Summarize.lmRatiotab.Var(model10.A, method2)),
#             1-as.data.frame(Summarize.LII(model10.A, method2))) #as.data.frame(getTaxCor.Tab(model10.A, method2)$V.tax), 
#as.data.frame(getTaxCor.Tab(model10.A, method2)$Median.tax),

#dtest<-data.frame("cat"=c(rep("PERMANOVA.Cat", 10),
#                          rep("PERMANOVA.F1", 10),
#                          rep("PERMANOVA.F2", 10),
#                          rep("PERMANOVA.F3", 10),
#                          rep("PERMANOVA.F4", 10),
#                          rep("PERMANOVA.F5", 10), 
 #                         rep("lm.model.median", 10), 
 #                         rep("lm.model.var", 10), 
 #                         rep("lm.median", 10), 
#                          rep("lm.var", 10), 
#                          #rep("Taxcor.Var", 10),
#                          #rep("taxcor.median", 10), 
#                          rep("LII", 10)),
#                  dtest)
#dsum<-ddply(dtest, "cat", summarise,
 #     raw=mean(raw),
 #     QSeq0.5=mean(QSeq0.5),
 #     QSeq1=mean(QSeq1),
  #    QSeq2=mean(QSeq2),
 #     QSeq3=mean(QSeq3),
  #    QSeq10=mean(QSeq10),
 #     QSeq100=mean(QSeq100)
 #     )

#library(tibble)
#dsum%>%mutate_at(vars(-cat),funs(scales::rescale))->test
#test<-as.data.frame(test)
#test<-
#ggradar(test)

#t(test)
#ds2<-melt(dtest)
#ds3<-melt(dsum)
#rownames(dsum)<-dsum$cat
#dsum<-dsum[,-1]
#library(fmsb)
#dsum<-as.data.frame(t(dsum))
#radarchart(ds2, vlcex=0.5, pcol=c("gray8", "gray35","gray48","gray65","gray70","gray87","khaki4"))
#plot(dsum)
#library(ggiraphExtra)
#ggRadar(ds3, aes(x=cat, y=value, group=cat))+facet_wrap(~variable)

We have found that sometimes in the reference there are substantive differences in the network between static and dynamic network construction; but that in subsampled data these differences are reduced. There is considerable variation in outcomes; and it raises a question of what characteristics of reference datasets lead to different outcomes when we apply the two network building methods. This is not a question we will try to answer here.

A couple post-script comments about interpreting metabarcoding output data:

It’s important to be aware of what metrics are robust to changes in methodology, and which are not. In general betadiversity is robust because the relationships of the dominant taxa have higher weight in most betadiversity metrics, and so their relationships tend to be easily captured and replicated in all analyses. However, alpha diversity is not like this. We have chosen not to address it in this software because in practice alpha diversity counts are heavily dependent on the type of sequence QC that is employed. We do not model sequence quality and do not try to address sequence QC. In general, we treat analyses that hinge on alpha diversity in microbiome studies as highly suspect because endogenous factors, like the presence of disease, will skew the taxon abundance distribution and affect the accuracy and comparability of an alpha diversity estimate. Alpha diversity estimates often rely on an assumption that either the sampling effort was the same; or that the taxon abundance distribution of one sample can be infered from other samples. So far, both of these assumptions are essentially never met. I’ll explain:

Sampling effort is not the same as sequencing depth. The principle of sampling effort is rooted in physical effort because it acts to standardize the counts by area or distance covered. This provides results that accurately represent changes in density of sampled species across sites. It is well understood that sequence data does not do this. However, there is a widely held misconception that taking the same number of sequences from a sample across the dataset (i.e. even rarefaction) does represent a standardization of sampling effort. It does not. It is the equivalent of doing a sampling of the rainforest and the temperate deciduous forest by identifying the first 100 trees we encounter. This approach would tell us nothing of the density of the respective trees; only give us information about the relative position of each tree within the species abundance distribution of each forest. To standardize sampling effort, we need an index of species abundance that actually embodies information about the abundance of the species. For example, if in this survey, we record how far we travel to encounter 100 trees, and finish our count calculation by dividing tree counts by the total distance we had to survey, then then we would have an output value that accurately tells us something about the abundance of specific species independent of the abundance of others. This is the key purpose of normalizing for sampling effort. Since we do not end up with a spatially explicit estimate of taxon abundance by using even rarefaction, it is not in principle a normalization of sampling effort. Approaches that do not infer a taxon density are difficult to reliably use for estimating alpha diveristy.

The taxon abundance distribution is often infered across samples. There are instances where this may be appropriate, however in most environmental microbiome studies it is not. Endogenous factors like the presence of a pathogen can result in a large change in the species abundance distribution at a single site. It may be possible, given ecological knowledge of specific members, to make such an assumption based on the known behavior and interactions of members of the community. But no software currently accounts for the ecological role of microbes in attempting to infer the species abundance curve of undersampled experimental units. Therefore, the current approaches to infering species abundance curves are inherently unreliable, and blind to the role that species interactions have on structuring the species abundance curve.

This is all to say: alpha diversity metrics in microbiome metabarcoding studies should be taken with a hefty grain of salt, and the analysis of these studies should probably not hinge on the alpha diversity estimates.